The rulebook of the Rue Morgue expansion, at page 25, includes crawlers in the extra activation rule when running out of miniatures.
The Zombicide Season 3: Rue Morgue box contains enough Zombies to invade a city. However, players may still run out of miniatures of the indicated type when required to place a Zombie on the board through spawning (including Crawler spawning!) or populating a building. In this case, the remaining Zombies miniatures are placed (if there are any), and then all Zombies of the indicated type immediately resolve an extra Activation.
A few pages before, on page 12, the rulebook uses Crawler Spawning to refer the way Crawlers appear when killing Skinner zombies rolling "1s".
1 – Crawlers can appear each time Skinners are eliminated. After removing Skinner Zombies, whatever the type (Walker, Fatty, or Runner), and earning experience points for the kill(s), add a Crawler for each “1” rolled on the attack roll. If you own Zombicide-themed dice, the “1” is replaced with a Zombie head. Read only the dice results: the +1 to dice roll Skills have no effect on Crawler spawning.
So crawler spawning refers to this way of adding figures. Anyway, when adding them through the bed card, extra activation rule activates too, as it's said in page 25, right above the "Running out of miniatures" section.