There seems to be a bug with the talent: starling spider from the vagrant skill tree. There is no cooldown if you simply let the spider die on its own instead of manually exploding it.
I've additionally done a bit of research on the enderal subreddit, and the SureAi discord. It seems this has been a bug for a quite a while now, only mentioned by a few users over the years.
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I know this is a minor bug and I am hoping there is a quick fix for it. I really enjoyed playing as a vagrant and really loved the ambushes you could set up with the starling dummy. But when i realized there was a cooldown bug, it really put me off from playing with this perk, because it became so easy to cheese/abuse with a talent that had no cooldown.