I know Fallout Tactics is not very well received here but when it comes to the theme of pre war robots emerging from a pre war manufacturing facility or Vault, I think its storyline and explanation for the robots is much better than that of Automatron.
In it Vault Zero's pacification robots eventually became a problem to everyone, regular wastelanders, Ghouls, Super Mutants, the Reavers, the Midwest BOS, as they spread across the Midwest to attack settlements in order to gather resources and reclaim manufacturing plants that could build more of themselves.
Is there any indication that settlements like Diamond City, Convenant, and so on are under threat of the new Mechanists robots?
Is for example that foundry occupied by raiders under attack by robots seeking to claim it to gather forge metal for new robots, or any of the other places that contain advanced technology that could be used for making new robots?
Or those satellite uplink stations, in order to expand their communication network the robots would probably attack those places to determine if those places can be fixed to extend their signal range.
The robots should have been as much of a threat to the Commonwealth as the people make out raiders, mutants, and synthetics to be. People would probably discuss among each other that the robots must also be operated by the Institute.