Not quite right either. The haywire synth mentioned on that page is the Broken Mask synth that shot up the bar in Diamond City.

What we know about the CPG is that the Institute helped them for four years, but was on the verge of giving up.

And then Nick tells us a synth murdered everyone.

So it's a little murky what happened. It's possible the synth was there as a representative of the Institute and just happened to be the last one standing after an argument turned into a gunfight. It's also possible the Institute decided they were done with things and did send synths to tie up loose ends.

But the CPG massacre was in the 2230s and the Institute has already kidnapped enough people and turned them into super mutants for a horde to attack Diamond City in the 2180s, so screw those guys anyway.