I just finished a tub/shower remodel and when I turn on the tub, water backs up and I get a slow drip from the shower head.

I have seen similar problems posted elsewhere with pex going down to the tub spout being the common culprit. I have copper going down to the tub spout and also to the shower head.

I originally used a moen shower/tub kit. I had a plumber come out to look at it and he confirmed that everything in the installation looked correct, so we concluded that I must have had a bad valve.

I replaced the moen with a delta kit, same set up, everything looks right, but the problem is still there.

2 different valves from 2 different companies, same problem. At this point, I'm wondering if its a problem with the cartridge.

I did not have the problem in the past with my old set up (hot and cold had separate handles)

Maybe a problem with the tub spout, causing too much back pressure?

It's not the tub spout. Whether it's on or its exposed pipe, it's the same problem

the pipe going to the tub spout too small? if you used pex, that is the problem..

Or CPVC, either one will restrict the flow enough that it will flow up and drip out of the showerhead.

He said it is copper, so neither of those is the problem. Maybe the valve is upside down, although should not be with two different valves.

I missed that part. Maybe your water pressure is too high, have you checked to see how much pressure you have ?

The valve is not upside down.

How would I check the pressure?

With our old set up(separate hot and cold knobs) the pressure was fine.

The 2- handle is a different animal than what you have now. You can get a cheap sill cock gauge to check the pressure. If everything else is right with the installation, the pressure is most likely your problem.

So if the pressure is too high, how can I reduce it.

You use a pressure reducing valve. Unfortunately that makes your system, a "closed" system, and you must also install a potable water expansion tank.

you didn't specify your dimensions. Distance from valve to showerhead and tub spout have to be within a certain range as specified by manufacturer. Are you within these constraints?

From the valve to the tub spout nerds to be at least 8". I'm at 9". Not 100% sure the height on the shower.

Height of the shower, OR the material for the riser, is immaterial for your problem. Even the drop to the diverter does not matter, unless it was very LONG or around a corner. The dimension they give you is to prevent conflict between the diverter spout and the trim ring around the handle.