The engines can still start at the same time while running off of the APU.
Suggestion: Program the packs so that when we turn the packs off for engine start the APU can only supply enough bleed air for 1 engine to start. Therefore if we pull on both engine start knobs at the same time neither engine would be able to start. This would lead to only starting 1 engine at a time which is what should happen. Off the top of my head the simultaneous engine starts, (2 engines at 1 time) while on the APU, only exist on the B777, B747, and B787 to the best of my knowledge. I do not know about the A350 or A380.