I can imagine are three ways the inrush current could be a reason for tripping the RCD:
One is that there might be a more or less weak connection between N and PE somewhere in the circuit - especially if the RCD was added later / lately to an old installation. With high load current the N voltage reaches enough voltage drop to drive enough current. Under Light load this might not be enough to trip the RCD.
During turn on and maybe also during turn off, there might be a significant DC current spike (
) from the SCR circuit part. Some RCDs don't like DC current that much and can trip from this, even if it flows the "correct" way. Inrush currents with large transformers can also reach really high values (e.g. 20 times nominal current) - this might trip the RCD by an unwanted side effect too.
Fast switching transients can also cause enough higher frequency noise on the line and this can give rise to higher than normal currents through the EMI suppression caps - the caps responsible may be even in other gear at the same circuit.