Does Zombie link trigger when out of models?
The rules as written state: The Survivor plays an extra turn each time an
extra activation card is drawn in the Zombie pile. (source).

This explicitly states that the extra turn is only gained when an activation card is drawn (those that say "all X 1 extra turn").
Note: this ability would also trigger at blue threat level, even though the zombies do not get an activation.

As stated in the comments though, it is your Zombicide game, so you can adjust the rules as you please. If you do decide to allow gaining extra turns from extra activations from having run out of zombie miniatures, I would recommend limiting the number of extra turns a surviver can get to 1 per round.