This is an obvious prediction of the ToE.
Well over a century ago it was noted that the ear bones develop like reptilian jaw bones.
The ToE says that if mammals were not around for all times then they developed from existing animals. When we look for likely candidates for mammals ancestors there isn't much choice but reptiles. In addition, the development pathways suggest that reptiles are a good candidate.
Therefore, we expect to find the various things which characterize the
modern definition of what a mammal is in various stages of transitions. This we have found.
The ToE predicts that there will be transitional forms between what are
currently end branches of the 'tree of life'. The early mammals, therapsids and reptiles before them are just such a chain of transitional forms.
As far as predicting the time frame it would be determined after dates are applied to know fossils NOT directly from theory. Then the theory can give a time frame to look in.
This is the case with Tiktalik. We had fish with some amphibian traits on one side of a 10 million year gap and amphibians with clear fish like traits on the other side of the gap. It isn't rocket science to figure out that somewhere in that 10 million years there should be something so transitional that we could no longer call it fish or amphibian (so the half joking -- fishaphibian). The theory then tells us where to look: where would selection act to push the path from fish to amphibian along? -- certainly not in deep oceans.
In the case of the MME we have fully developed mammals at one point in time. If there is going to be an evolutionary path to them (which the ToE predicts there will be) then the transitionals will be before the fully developed forms (duh!). Then just like the Tiktalik case we bracket the time from on the older end. These transitional forms would be after some of the precursors were already extant.
I think in the case of the MME evolution I don't think we had to focus so hard to find the transitionals.
The ToE does say that the DDME evolved partially in reptiles and then continued into mammals until it became what is known as the DMME in modern mammals.
This is correct, of course. If we
define a mammal as a vertebrate animals with a particular ear construction then
all of the development had to happen (but only by definition) in earlier pre-mammal forms. But that would be caught in a trap of thinking about things only from the current perspective. It is solved a bit by using the term as you have -- "modern mammals". The mammal vs non-mammal dividing line is over evolutionary time scales not so sharply defined.
It is similar in the Tiktalik case just as the ToE tells us. We had fish. We had funny fish with sort of legs. We had amphibiany like fish. We had fishaphibians that are so in between they are hard to put in either taxon. Then we had very fishy amphibians and less fishy amphibians. Once the lineages have gone on the independent ways for a few years (millions, 10's of millions) it is easy to draw taxonomic boundaries. It isn't so easy while the transitions are happening.
In the case of reptiles and mammals we used to call the therapsids "mammal like" reptiles. That term is now out of favour. I don't now why but maybe one reason is that we'd end up with (as we filled in more transitionals) with reptile like mammals. And, like in the semi facetious Tiktalik case above, all sorts of other "inbetween" forms. It seems the choice is to put something like a transitional taxon in between so we can put all the mammal like reptiles, very very mammal like reptiles, the reptimals, the very reptile like mammals etc into it. This appears to be the therapsids but I'm not an expert so I don't know.
Based on the evidence that we currently have, what would or does the theory predict?
It's too late. We have the fossils already. We know about when the transition was taking place. I think you want a Tiktalik like prediction that is done before the discovery. Like I said, that we would find the transitional forms was a strong prediction but when we would find them required some fossil record to fit them into.
What do you expect?