This is how I understand the reaction. Baeyer-Villiger reactions can occur under acidic or basic conditions. What is common to both is the O-O bond must be polarized such that one of the oxygens will leave taking the electrons between them. Therefore, the key to the migration is a donation of electrons to the other oxygen atom. If a RCH(OH)OOR" is created from an aldehyde, then the apparent migrating group is a hydrogen. I think of it as simply a loss of a proton and the product is carboxylic acid rather than an ester. If RR'(OH)OOR" is created from a ketone, then the group best able to donate electrons migrates. Here, it may be helpful to draw the intermediate as an -O(+). Then you may think about which atom can best donate electrons to it, namely a tertiary carbon is better than secondary, primary, or methyl.
For those following the mechanism, I like the analogy of the Baeyer-Villiger oxidation to the oxidation step in a hydroboration reaction. Boron, because it holds its electrons less tightly, can succeed in migrating all carbons. Carbon, because it holds its electrons more tightly, only migrates the most electron rich carbon. So it is the electrons of the original carbonyl group that you must focus upon. It is the most electron rich bond that migrates. Carbons donate electrons to a tertiary carbon increasing its electron density. I interpret CH bond to go by a proton loss. That is the general mechanism of an oxidation reaction.