We should never underestimate the wealth of ideas for physics beyond the Standard Model. It is definitely a very wild area ;)
I will try to answer your question, but please note that this lies a bit far from what I do, so that my knowledge on this topic is very partial.
Right after sending my initial comment, I thought about the following. I assume that after the big bang, the universe first had to cool down below a certain threshold so that black holes could even start to form. Therefore, a precondition for the primordial black hole theory would be that the inhomogeneities can not have started to materialize before the temperature hat fallen below that temperature.
That's correct. We need some gravitational collapses for the primordial black holes to form. Note however that this happens well before stars were formed, so that this has nothing to do with the way "usual" black holes are formed. We need obviously a trigger, that either materalises itself as a quantum fluctuation of the energy density of the universe, or relies on a more fancy models (those even exist ;) ).
So my next question would therefore be, do our computational models produce enough temporal resolution to be sure regarding the order of these events? Or does this thesis still require to simply assume that black hole formation preceded the inhomogeneities?
I am afraid I didn't get this question. Sorry... Do you mind clarifying / elaborating?