The tap switching with relays in linear power supplies is usually not made to be switching very often / fast in a squence. The relay contacts see quite some load as there is some filter capacitance to charge. This may cause wear and if in fast sequence also possible sticky contacts from overheating.
If just at the edge, the additional load can be enough to let the raw voltage drop enough to make the supply switch taps. Nomally the hysteresis in the control should be large enough that this should not happen. The supply going to limiting mode and than with a lower voltage going to the lower tap could also be possible. One could test the hysteresis of the tap switching (e.g. without load), maybe it is a bit on the low side.