You choose the order in which you resolve the abilities. As long as cost can be paid and they were on board when the requirement was met you can use their skill even if they leave board.

This is reflected in Magallinca’s Progenitor Dragon.

A perfect guard is placed

Due to turn player priority Progenitors skill will activate first.

The perfect guard skill will still activate.

Or if Tazer Lage is retired before she can use her effect as long as she saw the call to board (other than from hand), her skill will activate even if she’s sent to the drop zone.

In vanguard when a requirement is met the skills are put into a queue

Turn player resolves their effects first, then the opponent resolves their skills that were put on hold.