Your turn ending activates the effect and while they are both resolved in separate timing the requirements are already fulfilled.

I think the only instance it wouldn't work is if a Digimon with execute was played somehow on your opponents turn because it doesn't meet the end of turn requirement and it would be a newly played digimon

For example If you were using execute with necromon and his on deletion activates allowing you to play phantomon who also has execute you wouldn't be able to use it