A tstat probe never goes in a cage when it is being used to control a uth.

It needs to be against the uth and can either be between the uth and cage floor or on the bottom of the uth.

I don't know the size of that probe but if it is large it is many times best to put it on the bottom of the uth so you don't create a cool spot in the center of the hotspot by keeping the uth off the actual cage floor.

When you attach the probe tape the wire just behind the probe and the tip(if necessary) to keep it in place. Usually the weight of the tank will keep the probe against the uth and taping the tip is not needed.

Aluminum duct tape is the absolute best tape for the job as it doesn't melt, stretch, and decay like many other tapes.