I would say that the mechanism you have drawn cannot be correct, because the rearrangement you have drawn proceeds through a cation in a solution containing methyl magnesium bromide.
I like your first mechanism better.
I cannot say categorically the mechanism is correct, but it is consistent with an increase in MgBr2 increases rearrangement.
Although it is unusual to see a carbocation in Grignard mechanism, let me remind you that formal charges are simply bookkeeping devices as no change in charge ever occur, protons are positive and electrons negative. The charge being written is more commonly an indicator of the importance or motivation of one chemical species over another. A Markovnikov addition could be written as concerted (as you might find with hydroboration), or bromide addition to generate the more stable carbanion, or by protonation. While Markovnikov himself simply noted the halogen was added to the more substituted carbon, we now believe this occurs because the key step is the addition of a proton to an alkene. Initial protonation certainly it is more plausible as bromide is a much weaker base than a carbanion and its formation from a bromide would require climbing a large energy hill. Therefore writing a carbocation is telling you the magnesium is pulling the electrons away from the carbon. While that is unusual, given the greater strain of an epoxide, greater electrophilicity of magnesium, seems plausible.
Disco referred to the allyl alcohol formation from an epoxide. If the mechanism were to proceed by this mechanism, this mechanism consumes Grignard. Although a carbanion can be recovered at a later stage, doing so invites formation of by-products to compete with the methyl anion. Base opening of an epoxide is a known reaction catalyzed by diethylamide. It does not give an aldehyde. The rearrangement of an epoxide can occur with a Lewis acid, including Grignard reagents, but not alkyl lithium reagents. One might think if the rearrangement were base catalyzed, this rearrangement could be found with other bases.