Rates increase for every 5 summons, not only if you do the 5 stones straigh but also if you stop the session, watch here for example https://youtu.be/Gx-9WpP0HdgMaybe I'm misremembering but I did it previously and I'm pretty sure the chances increase even if you don't do all 5 from the summon sigils.
EDIT:
Ah. Perhaps I'm remembering wrong. Damn I'm a fucking dumbass.
At 3:34 he only summoned 3 units and got the 0,25% increase on 5* focus and normal 5*.