I understand this might be a dumb question as I have been laughed at for asking it. but.. my car is revving high (I'm repairing that issue tomorrow when the weather breaks) but yesterday when I started the car and it revved high (sorry no tachometer display so I don't know the exact rpm - just going off sound here) I heard the pump move more fluid than normal. Then when I went to leave work never heard the pump kick on and temp crept up (not to red but def high). Is it possible the aftermarket pump was damaged by this? Trying to see what I need to replace or if it could have caused another issue or just completely unrelated. 05 Impala
Really, this is not a concern. The coolant pump is designed to spin as fast as the engine goes. Revving the engine up is not going to cause it any issues. That's for either a true OEM pump or an aftermarket one.
As GdD stated in the comments, most stock (and stock replacement) pumps are driven directly off the engine, so there's not going to be an on/off with them. They are designed to push fluid while the engine is running. There are some vehicles which have electric pumps and push coolant around after the vehicle is shut down. This is to help with even cooling after engine shutdown. Your car is not one of those.
This is definitely not a dumb question. It's one of those "if you don't know, you don't know" questions. That's what we're here for, so ask away.