That is a good point, and I have been thinking about issues like that. At the expense of some possible story spoilers, we can discuss that here. 

Basically, I was thinking that in the story (at least in the first) at the beginning there would only be two pokemon: Mew, and an unfinished Mewtwo, Mew is a creation of the Nazis during WWII, while Mewtwo is an attempt to replicate Mew. When our characters eventually find Mew, they will find that (similar to a chicken) it lays eggs every so often (for it's "period"). By manufacturing a "sperm," they will artificially fertilize Mew to create the first different pokemon species. In creating these sperm, they would use genomes containing different radioactive compounds that would randomly produce different pokemon (however the same radioactive compound will always produce the same 'type' of pokemon). This is at least in part supported by Pokemon lore because according to bulbapedia: "Mew is said to have the DNA of every single Pokémon contained within its body." 

Similar to what Frankenmouse was saying about unstable molecular structures, as the radioactive compounds within pokemon genomes successively stabilize, the pokemon will evolve. I know (actually think because its been a few years since Chemistry) that it can take hundreds/thousands/millions of years for radioactive material to stabilize, so perhaps something within the pokemon themselves (or the use of their powers) could contribute to catalyzing these stabilizations (though I think radioactive elements always take the same amount of time and can predictably be used to age mateials? Don't quote me on any of the science). 

I know the science is shaky (and sometimes just plain wrong), but I figure it is believable-ish enough. These details will really only make up a few posts, and I'll be sure to make them sound super science-y when delivered by Birch and Oak. The realism will come more from the mature setting, story, and characters than the science of the pokemon themselves. 

As a side bar, I don't feel like the Oak set forth in my background would try and artificially make more pokemon after everything that went wrong with the first two, so Birch would be the one who does all the artificial insemination stuff.

What do you guys think?