Aloha,
So the 20 battles number came from the initial release of this update, MM attempts to ensure that no more than 40% of 20 battles at each tier are uptiered.
This can be overridden by time in que (as most MM rules can be).
So this means for Tier V, tier VI and tier VII it will attempt to only uptier EACH tier a maximum of 40%
So if you play say 5 battles at tier V then 5 battles at tier VI and 5 battles at tier VII and that is it, it IS possible to be uptiered for 15 battles.
Conversely, let's say you intend to just play tier V and you have played 8 battles so far and have been uptiered for all of them, then assuming you aren't in que too long to where rules start getting overridden, your next 12 should be tier V battles.
Mahalo,
-Hapa