With circuit off, why would neutral wires spark and lights on a different circuit flash?

70 year old house with a breaker panel that was upgraded from fuses about 20 years ago. A couple new circuits were added at that time for the kitchen and laundry room, but the wiring in this particular situation is all the original.

Replacing a ceiling fixture, I turned off the breaker for the circuit that the fixture is on and removed the old fixture. There are four white neutrals bundled together into a old rusty wire nut (I have a new red one ready to go,) and a single black hot wire. This box is controlled by a single switch.

I removed all the wire nuts and old mounting bracket, and was screwing in the new mounting bracket – nudging the bundled neutrals around in order to do so – when there was a tiny spark on the neutral tips and lights on a nearby circuit flashed. Happened so quickly I wasn’t sure I hadn’t imagined it.

I jostled the neutral bundle around a bit and no reaction, so I continued. When I went to pull the neutral bundle through the new bracket in order to get ready for the new fixture wire, a definite spark flew and the lights on that nearby circuit completely went out. Wiggled the neutrals some more and power was restored to the other circuit.

Promptly put the nuts back on the exposed wires and let it be. Time to call a pro but what would be happening here? I’ve been in this house for 30 years and have personally replaced all the fixtures, plus most switches and outlets at one point or another and I have never run into an issue like this. Am I correct in guessing that the neutrals on this circuit are in contact with a hot wire on that adjacent circuit – either by loose connections, or worn insulation?

Thanks,
Jamie