I've been playing that they enter play normally (when Nyarlhotep is the GOO) but after they're defeated they go back into the monster cup without becoming player's trophies.
Is that it?
On the back of the Mask Monster marker, it tells you what you do with it after you have defeated it.
"Return this marker to the cup."
In the rules under Setup, it tells you how to use the Mask Monster markers during the game.
"If Nyarlathotep is the Ancient One, add the Mask Monster markers
(the Monster markers with a mask symbol on them) to the monster
cup. Otherwise, set the Mask Monster markers aside and do not
use them during the game."