OK, got it.
I assume it runs at 230V, and the transformer is the one mentioned..
That transformer has to be on because it runs the start circuit, for which there must be power to close the contactor. Not an issue, if set to the right voltage, AND if sized for the contactor load. It looks small for mist any AC contactor, but I do not know that at the present time.
One issue is whether the transformer is the right size and voltage tap.
Another is this business of the voltage not shutting off when the RPC is shut down. I would solve that first. That has to happen for safety. Your plug connection will serve as a "disconnect" for any individual machine, but the shutoff thing needs solved.
After that, the contactor needs to be assessed for it's "VA" draw for both closing, and maintaining closed. The transformer you have there, which appears to be a replacement, looks, as I said, considerably too small. it looks like only a few "VA" in rating, and may be just not sufficient to do the job.
Bigger ones are available from suppliers such as Digikey and Mouser Electronics. But you need to know what the contactor draws. That number may be available from the paper you have that you posted a pic of. The fuse value for that fuse associated with the transformer will also give a good clue.