Pure speculation but perhaps they’re simply individuals who the Ascians recruit that aren’t shards of the former Convocation. The Convocation members would use the red as it’s a tradition. The hierarchy would then be something like:

Unsundered > Sundered Convocation members > Random Sundered Ancients.

In that way not using the white masks could also be a way to reinforce the inferiority of the Sundered. They don’t get to use those because “those are for the Ancients and you aren’t them yet.”

That’s at least an in game explanation, I agree with Mikko on why it’s that way from a meta standpoint.