I'm with Bob and Tom here.... You probhably notice a "ping", or "pong" when you flip the switch? How many watts are you running on each transformer?
Are you using a decent "lighting" Transformer, or one of those buck and boost T's with a few modifcations of adding CB's from a "Manufacturer". Some of the cheaper ones will just modify a buck and boost. That will give them a very high in-rush. (As they were designed for power, not lighting...) You can try the breaker suggested, or if possible use a dimmer to ramp up the switching current, or switch seperate.
"Well - I oughta....." -Jackie Gleason