Puller I have is Mac Tools PP40. Installer is a Snap-On CJ113B3. It requires a threaded shaft.

I'd buy used US made good stuff on ebay before fooling around with the China junk.

The loaned stuff at the auto parts is the same Chinese junk the Horror Freight sells. It usually breaks or ruins the pulley before you get it off. Pinching the jaws of the puller together in a vice when it is installed to remove the pulley helps prevent it from jumping out of the groove. Or you can use the cup style.

I see some of this stuff on ebay now. Not cheap, but not new price. Buy it, use it, put it back on ebay if you don't want to keep it.