So, in Heart of the Swarm, we get to see Zerus in-game. Zerus itself was only described in the manual beforehand, but it did leave a clear impression of what the Zerg left behind.
This created a discrepancy between the manual that described Zerus and what we saw in Heart of the Swarm. A lifeless world versus one full with the lives of Primal Zerg.
So, this is my hypothesis to explain away that discrepancy.
Let's start with some quotes:
"Travelling thousands of light years into the burning core of the galaxy, the Xel’Naga eventually settled upon the volatile ash-world of Zerus. The Xel’Naga planned to continue their Grand Experiment of evolution, only this time they dismissed their tenets of physical form and focused chiefly on the pursuit of a distinct purity of essence. Residing in their massive ships high above the fires of Zerus, the Xel’Naga began once again to challenge the wiles of fate.
The Xel’Naga were more successful with their second venture than they could have imagined. They laboured to advance the evolution of the most insignificant life form on Zerus, a race of miniature insectoids known as the Zerg. Through Xel’Naga protogenetic manipulations, the Zerg survived the torrential firestorms of their world and thrived. Although extremely small, wormlike, and possessing no ability to manipulate their physical surroundings, the Zerg adapted to survive. They developed the ability to burrow into the flesh of the less vulnerable species indigenous to Zerus. Feeding off the nutrients contained within the spinal fluids of their hosts, the Zerg learned to parasitically merge with their host creatures. Once they became capable of controlling the metabolic and anatomical processes of their hosts, the Zerg used their new bodies to manipulate their surroundings." - Manual
"The Xel’Naga soon made an alarming discovery. The original races assimilated by the Zerg were hardly recognisable after only a few generations of their inception. Somehow the Zerg had developed the ability to supercharge and steer the latent evolutionary processes within their host creatures. The host creatures fell prey to the effects of gradual physical mutations that caused all of the various strains to grow armour piercing spines, razor-sharp limbs, and ultra dense carapaces. Over a surprisingly short amount of time, the strains grew to resemble a terrifyingly ravenous and unified race." - Manual
This would be the Zerg before the hive-mind was created. This last paragraph is describing the beginnings of the Primal Zerg.
"The Xel’Naga, remembering all too well that their failure with the Protoss was a result of pushing the sentience of the fledgling species too quickly, decided to follow a different path with the burgeoning Zerg. Attempting to waylay the potential hazards of differing egos, the Xel’Naga structured the collective sentience of the Zerg into a unified, amalgamated ‘Overmind’. The Overmind coalesced into a semi-sentient being that represented the primary drives and instincts of all of the Zerg strains. As time passed, the Overmind developed the rudiments of personality and advanced intellect." - Manual
This is the creation of the Overmind, and the "corrupted" Swarm Zerg.
"As the swarms continued to grow and strengthen, the Overmind turned its thoughts towards its own future. It realised that within a few short centuries its race had assimilated all of the indigenous life upon Zerus."- Manual
The Zerg have assimilated all life left on Zerus. There is nothing left but the Zerg.
"Drawn to the barren world by this beacon, they were quickly assimilated by the swarm." - Manual
"The Zerg left the lifeless, burning world of Zerus..." - Manual
When they leave Zerus, the world is left lifeless, burning, and barren.
When Kerrigan goes to Zerus in Heart of the Swarm thousands of years later. 
The most prominent environment is rain-forest, and the world is full of Primal Zerg.
Many fans I've come across claim this is a "retcon" but I don't think it is.
So, the Zerg Swarm under the Overmind was in space for an unknown number of years conquering hundreds of worlds. We know the Overmind has been around for several millennia. Not all of that time has to be solely on Zerus. We don't know when the Overmind actually developed the psionic ability to create wormholes for FTL journeys, so he could have been making STL journeys between solar systems, at least for the first few conquered worlds, or been limited to a slower form of FTL. Eventually, they get to the point where they have the 60 year journey to the Koprulu Sector from discovering the Terrans.
The point is that a lot of time passes.
Well, how is this suppose to fix the issue?
We have a few answers to this issue.
A) The first spawning pool still exist on Zerus. Therefore the place where the Zerg first evolved still exists.
The world can still be lifeless, but be in a state that will eventually produce life.
B) The world is stated to be lifeless in the sense there is no noticeable amount of bio-matter left. Lifeless in the dictionary can actually mean "apparently dead" rather than just dead. The spawning pools still left could still contain Zerg micro-organism from which the Zerg could evolve from.
C) There is still one problem left, but that problem can also be an answer. Zurvan stated he was older than the Overmind, avoided Amon's corruption, and remembered the Xel'naga. How can the world be described lifeless if he is alive? We get back to that "apparently dead" definition. Zurvan in his very first appearance demonstrated the ability to go into a deep hibernation state in which he would sleep until he could encounter new unique essence to consume. Him entering this state, and staying in it for the last years the Swarm were originally on Zerus would fix this problem.
A word we can apply to this state is anabiosis, which has the following definitions:
- 1. (Zoology) the ability to return to life after apparent death; suspended animation
- 2. reanimation after apparent death.
- 3. Zool. a state of suspended animation under adverse environmental conditions.
This state would fit with how Zerus is described in the manual and how Zurvan could live before and after that period.
Given Zurvan showed the ability to spawn Primal Zerg by quasi-regurgitation during his boss fight, you have another possible source of the Primal Zerg's resurgence on Zerus.
Now we're faced with the main issue. If the Primal Zerg had to start off by evolving either from scratch or from micro-organisms, with Zurvan staying in a hibernation state rather than Asexually reproducing more Zerg, how does the planet become so full of life in such a (relative to evolution) short time frame?
The main answer to this comes from Stetmann's research log of what the Zerg can do at the cellular level, which is evolve in a single hour faster than humans did in 100,000 years.
So, assuming that 100,000 years is a standard, that's 876,000,000,000 years of evolution in one millennia, add the few more millienia, and you have trillions of years of evolution. More than enough time for Zerg cells to fully populate Zerus from the micro-organism stage.
You might argue that the Primal Zerg's cellular structure may not be as advanced as the Swarm Zerg, but this is what Zurvan states about the first Zerg microorganisms:
"It existed before names. From this primordial place, the zerg arose. Within, one essence split into many. One devoured another and became stronger. The first zerg." -Zurvan
Which fits pretty neatly with what Stetmann says here:
"There is a basic dichotomy to zerg cell reproduction. Type A cells throw off seemingly random mutations. Type B cells hunt down these mutations and destroy them. It's survival of the fittest on the cellular level. Successful mutations thrive."
The only big difference is the Zerg micro-organisms on Zerus having the capability of taking another micro-organisms essence.
So, the world was lifeless. Now it's full of Zerg bioforms.
Because of the reasoning above, I believe the Zerg managed to do this either because they evolved from either the Zerg micro-organisms left on Zerus, the spawning pool starting back from stage one with evolution, or Zurvan spawning a few primal Zerg.
All of the above could possibly happen at the same time as well.
For a minor issue to resolve as an addendum, the manual describes the Zerg as looking generally the same. This would mean their insect-like Swarm appearance.
Given that other microorganisms spawned other life on Zerus, before the Zerg's bio-engineering upgrade, and they formed their own biosphere before they were assimilated, this can explain some of the reptilian and mammalian Zerg rather than the insect-like Zerg described in the manual. If their cells were consumed on the micro-organism level and incorporated into the Zerg microogranims.
This would explain the Primal Zerg having a vast amount of variation in the appearance of their strains compared to the Swarm Zerg, I.E. Flora Zerg (Zerusian stingers are forms of Zerg, suggesting that the Plants on Zerus are Primal Zerg), the Mammalian Zerg (The Quilgor), and the Reptilian Zerg. (Most of the Primal Zerg we see)