I agree. A typical three-phase starter isn't going to have a grounded conductor ("neutral") for a motor load. Was the coil in the old starter bad? If not, I'd swap them since my guess is that you are sending 208 volts into a 120 volt coil.
The starter that you replaced may have the same part number, but someone could have changed out the coil in the field for a standard three-phase 120/208 installation. I can't begin to imagine how many times that I have done this at gas stations and car washes.
"But the guy at Home Depot said it would work."