1st, it’s Jimmy Thompson – The character Michael (played by Ari Millen) delivers a message before committing a murder and he says – “Jimmy Thompson sends his regards”. And the Connection to Paul: The bartender, Paul (played by Peter Outerbridge), realizes upon hearing the name that Jimmy Thompson is an underworld/crime boss from his past, and that Paul—not the person who got killed—was the actual intended target of the hit. Does that make sense?

I always took that scene to mean the calls were coming from the bartender’s accomplice — or possibly from someone connected to the murders he was covering up. The whole point of him lying about the phone being dead was to isolate Steve and control the situation inside the bar.
The movie never gives a completely explicit answer about who was on the other end, which is part of what makes The Oak Room so tense and unsettling. But the implication is that the bartender absolutely knew the calls mattered and didn’t want Steve answering them because it could expose what was really going on.