Attic expansion with OSB and vapor barrier

Where should the moisture come from? Humidity from outside? That is not a problem. Cold attic and moist air from the upper floor would not be good, but you do have a vapor barrier installed.

then moisture can get under the OSB boards in summer, right?

Yes, that's correct. But the enemy is not "moisture," it is "condensation."
As long as the dew point is not undercut in your top floor ceiling in summer, you don't have to worry (and it definitely won't be!).

The problem with OSB in summer is much more the prevented or hindered redrying of the insulation from moisture that may have accumulated there over the winter. That's why my advice is to have generous joints and spacing when laying them.