Unless these fans are monster power hogs as in 8 amps each or more....
Your saying that the lights don't share hot or neutral with the beds and are actually fed from a different sub-panel.
If the wireing is in fact completely discrete from the bed wiring then the only thing I could offer to look at is the neutral capacity/connections.
How two tiny fans starting could affect the tubes in a Recessed can when fed from a different subpanel I don't know. But my first thought would be to look at the neutral connections of the panels/service
