Yes, saccharomyses. But more often, it is debaromyces or kluyveromyces, and goes likes this:
Kluyveromyces deacidifies surface some in 1-3 days. It's fast
Then a geo or a penecillin type will start a bloom in 4-6 days, finishes that pH increase up past 6.5.
Then the geo will die off and the b linens will feed on it. The b linens starts about a week into it. B linens MUST have the right food and pH to grow. This includes pantothenic acid. Yeasts produce this naturally. If you were to raise the pH up somehow to 7 on the rind, but didn't have the right food, the b linens still wouldn't grow.
Francois is right, IIRC, the geo strains have different levels of protection against contamination. Geo 13 is helpful for protecting against mucor.
To get a good b linens growth, you either need a tuned cave and smear the culture from an existing cheese to a new one, and then wash it (this is how the smear rinds were originally done), or add some geo or a complex mix like PLA to your b linens 3% wash to help deacidify the surface and pave the way for b linens.
 If the geo runs away and you start getting a slip skin, you can switch to a higher salt % brine, to a 8-10% with just b linens. Geo doesn't like the high salt % and will die off and the b linens can grow on top of it.