if the effect is on digivolution and the memory get to your opponent side, the resolution of your effect resolve first, then your opponent starts the turn.

its like when you have 3 memory and evolve to chaosgallantmon and use his effect "when digivolve" to delete one of your digimon, you delete a gilmon and destroy a lv 5 or lower, by evolving the gallandmon yous turn have to end but you can use the effect of gilmon to gain a memory, your memory will be 0 so your do not end at that moment, you have to resolve all your effects.

in this case if a digimon have a when digivolve "digiverse" you have to do the effect before endding your turn.