just bought a rental property and found that if the bath faucets are turned on high, water starts coming out of the shower head without the diverter on the spout being pulled. new spout has been installed

Sounds like a restriction in the pipe feeding the spout. If it's galvanized, maybe it's rusting up or if it's pex/cpvc, it's too small in diameter. Or, if there was a shower restrictor in the control valve, it's missing or the valve installed upsidedown.

straight piping from both hot and cold water valves to faucet and shower pipe. thinking whoever put in shower sized pipe too big

does this happen with the spout removed ??

Pipe size is NOT the cause of it. Pipe type may be the reason. But there are several possibilities and would have to be there to diagnose them.

Excessive water pressure can cause this also.

Haven't checked with spout removed. Currently on vacation, will check when I get back and let you know

what do you mean by pipe type? currently galvanized, but was figuring on replacing with copper.

If the hot and cold faucet supply lines have shutoff valves you can close down the shutoffs to a point that water flow is not as high but still adequate. If that stops the water from coming out of the shower head then you know it is caused by too much pressure or volume from the supply lines. You can also add a screw-on chrome shower head shutoff valve inline with the shower arm, keep it shut off unless taking a shower.

Here's one example:





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