Bill Vallicella poses the following problem: 

Consider a time t before there were any human animals and any finite minds, and ask yourself: did the nature humanity exist at t?

Vallicella points out that, for Aquinas, the answer would be that at t humanity existed in God’s mind. He comments on Aquinas’s answer thus:

This may seem to solve the problem I raised.  Common natures are not nothing because they are divine accusatives.  And they are not nothing in virtue of being ausserseiend. This solution avoids the three options of Platonism, subjectivism (according to which CNs exist only as products of abstraction), and Meinongianism.

What Vallicella is talking about here, of course, is Aquinas's doctrine of divine ideas. But he isn’t satisfied with the solution this doctrine offers.

The problem with the solution is that it smacks of deus ex machina: God is brought in to solve the problem similarly as Descartes had recourse to the divine veracity to solve the problem of the external world.  Solutions to the problems of universals, predication, and intentionality ought to be possible without bringing God into the picture.

I don’t see any reason to concede this deus ex machina (DEM) objection against Aquinas's doctrine. Why ought solutions to the problems of universals, predication, and intentionality to be possible without bringing God into the picture? Vallicella doesn’t say.  What if I instructed you in the following way: “Solve the problem of human knowledge without appealing to an immaterial intellect”? You could legitimately ask why I’ve barred the path of inquiry in this way. What if our reflection on the evidence indicated that an immaterial intellect had to be a part of the solution? (If you’re a naturalist, suppose I tell you to solve the problem of human knowledge without appealing to the brain.) Vallicella needs to explain why God can’t be involved in the solution of the above problems.

Vallicella references an earlier post where he considers what’s wrong with arguments that rely on a DEM. Let's look at this post to see if we can find out why he wishes to object to Aquinas in the way he does.

Vallicella suggests in this post five possible ways to understand what is meant by the DEM charge when it is leveled in philosophy. Vallicella’s DEM catalogue, however tentative, is very useful and appears to fill in a gap in the literature. Here are the possibilities he proposes:

(1) Any appeal to a supernatural agent in a theory of natural phenomena is a DEM.

(2)  An appeal to a supernatural agent in a theory of natural phenomena is a DEM iff no independent reasons are given for the existence of the supernatural agent.

(3)  An appeal to a supernatural agent in a theory of natural phenomena is a DEM iff no reasons are supplied for the existence of the divine agent.

(4)  An appeal to a supernatural agent in a theory of natural phenomena is a DEM iff EITHER no reasons are supplied for the existence of the divine agent, OR the working of the agent violates natural laws.

(5)  An appeal to a supernatural agent in a theory of natural phenomena is a DEM iff EITHER no reasons are supplied for the existence of the divine agent, OR the working of the agent violates natural laws, OR the agent’s intervention in nature is miraculous in the sense in that it takes over a job that ought to be done by a natural entity.

Vallicella doesn’t think we should a priori rule out arguments to God as the cause of natural phenomena. So, he says that (1) can’t be what a DEM is. (Actually, he doesn't argue exactly like this but this is how I interpret him.)

Vallicella also concludes that (2) can’t be what a DEM is. Here's how he explains its flaw:

Why would the reasons for the supernatural agent have to be independent, i.e., independent of the job the agent is supposed to do? Suppose the appeal to a divine agent takes the form of an inference to the best or the only possible explanation of the natural explananda. Then the appeal to the divine agent would be rationally justified despite the fact that the agent is posited to do a specific job.

I’m not quite sure what Vallicella’s view of (3) is. He seems to think that it constitutes a DEM but isn't the only form it can take. It can also take the form of (4) and (5).

But if we construe DEM as (3), (4), or (5), Aquinas's doctrine of divine ideas isn't conspicuously guilty of DEM. Aquinas doesn't fail to offer reasons for the existence of the divine agent whose mind contains the ideas (cf. ST, Ia, 2, 3). There is no obvious way that the doctrine of divine ideas violates natural laws (presumably the laws of the physical world that the natural sciences investigate). And, finally, it doesn't give a job to God that ought to be done by a natural entity.

With respect to the last point, Aquinas takes the divine ideas to be God's understanding of his essence as imitable by any creature (cf. ST, Ia, 15, 2). No natural entity as such could have God's understanding of his essence. Ergo, God isn't doing a job some natural entity should do, for no natural entity could do it.

So, I'm perplexed by Vallicella's suggestion that Aquinas's doctrine of divine ideas is an instance of DEM.

Vallicella is a careful, sharp thinker, so I assume that I have misunderstood him or he has only incompletely expressed himself. It’s possible that we do simply disagree but I suspect that the point of disagreement has not yet been identified.