Forgive me if I'm telling you something you already know, but thought I'd throw this out. I've found that with some inexpensive scopes they sometimes don't like to make immediate tracking movements. Some inexpensive scopes won't move until a couple of rounds have been fired and the recoil jars them into movement. Since a 22 has virtually no recoil, this movement may not happen for several rounds. Should you find that your new scope doesn't track immediately, you might give this a try. When adjusting your scope, with an empty chamber or fired cartridge in the chamber, make your adjustments and then from a height of 2" or so, drop the rifle on the buttplate/recoil pad. If your stock doesn't have a recoil pad, put down a towel or something to cushion the blow. Repeat this 2 or 3 times. This will jar the scope into moving the crosshairs where you intended them to be and will help save ammunition and frustration.
Hoss