I recently changed from a old style hot/cold taps, to a Moen single handle tub controls.

I've noticed now while the tub is filling and the control is mixing the shower head leaks a little. This only does it when it's mixing not when only hot or cold is running. Could the cartridge be damaged? Previously this did not happen.

You are in need of washer changes
To both taps!

This could happen if the house pressure were too high. Purchase a hose bib pressure gage,(see image) and let me know what the reading is.
Back tom you, Tom

LOL after looking through the search results how did I know you'd post that Speedball

Hello Shawn,

Try as Tom suggested, the range of normal residential water pressure is from 30 to 80 psi. Ideally, the pressure should be set between 45 and 60 psi in most residential plumbing system. If the pressure rises too high particularly above 80 psi, plumbing fixtures and appliances (primarily hot water heaters) could be damaged or leak excessively, also please tell us if you have a water PRV installed see the image below.

If the pressure is OK and you have a PRV installed then you may need to clean or replace the cartridge, click back if you need help how to remove the cartridge and we will help you, Good luck.

John

Just out of curiousity what's the difference between this new tap and the old one? Is this a low consumption/flow problem?

LOL after looking through the search results how did I know you'd post that Speedball
Here'a another! If the spout were to produce a little back pressure that could that could alsomake thye water level raise in the shower raiser.

this a low consumption/flow problem? If it were "low flow" you wouldn't be having this problem.
By the way, When you changed out the old shower valve did you cut and shorten the shower raiser a bit? Just asking! Tom

Here'a another! If the spout were to produce a little back pressure that could that could alsomake thye water level raise in the shower raiser.
If it were "low flow" you wouldn't be having this problem.
By the way, When you changed out the old shower valve did you cut and shorten the shower raiser a bit? Just askin! Tom

This is what I'm thinking it's doing, what would be the way to correct it if this was the case (please don't tell me I have to rip out the wall and tub surround I just put up).

The shower raiser is the same length as before, there was no reason to change it.

Let's find out what thehouse pressure's first. Tom