We have installed a new tub faucet. When the lever is pulled to allow the shower to work, the faucet sprays water.

If this is a new installation or someone has removed the lever and put it back, take the lever off.
There should be an plastic insert with grooves and a stop on it, which allows the lever to only go so far.This is removable. The insert acts as a stop to prevent scalding. you should be able to pull it out and reinstall in with the stop more toward the left allowing the lever to go more toward the hot side. Hopefully this helps out.

If flow is slow to shower,pull showerhead,small watersaver hole and screen have garbage in it,teflon tape-rust sand etc Tub spout working fine?

its because that model usually when u pull for the shower is not properly connected. You will have to remove handle and coverplate, then shine flashlight down to see what is happening when pulling rod on tub spout for shower. Usually its broken or bent and just needs new one installed. It cost me 2 buck for new shower rod. Directions u can get free from Moen with free lifetime parts.

You can cap the lines at the tub faucet to rule out tub faucet. It maybe mixing there.

Faucet may be bad also the safety stop will alow you to change water temp it can be tricky to adjust water temp.

check the tub faucet the pull lever maybe slightly faulty causing back pressure in line and pushing water up to shower head --u may have debris in tub line causing partial blockage -or u have alot of water pressure coming in and it is to much for the lines to handle and it is pushing up to shower head

You have more water trying to come out of the spout than the diverter gate will allow so by default it find another path of least resistance which is up the shower pipe to the head. I would suggest just getting a new tub spout. Remove it by unscrewing like you would a jar lid or it may have an allan set screw underneath and towards the rear.

Hope this helps and good luck.

maybe it is just a bad design,somethings look better on paper that they do in real life sometimes.good luck with yuor project.

Remove hot/cold button in handle, remove screw/pull off handle. Remove the two screws in the wall plate/remove plate. Use a wrench to remove the diverter assembly. Get new diverter assy and reinstall eveything. You don't need to turn off the water.

Sounds like it was installed upside down or the cartridge is installed improperly

Verify the height from the shower valve to the Shower head, the instructions specify the correct distance if it is too short the pressure could be getting up to the shower head.

Perhaps the water pressure it too high at the valve not allowing all the water down the faucet outlet, there are set screws on the sides of the shower valve to adjust the water allowed in the mixing chamber.

Something is restricting the water flow to the faucet, creating enough pressure to send some of the ater supply up to the shower.

I hope some of these ideas help