this is a simplified version on how the EP works.
Follow this, as Paul Kite put it:
Breakdown of the End Phase:
1) Turn Player can take an action or pass. If s/he takes an action, restart this list.
2) Opponent can take an action or pass. If s/he takes an action, restart this list.
3) If the Turn Player has yet to perform an action s/he is obligated to perform during this End Phase, s/he takes such an action. If not, s/he passes. If s/he takes such an action, restart this list. (Such as your Lightsworn milling)
4) If the Opponent has yet to perform an action s/he is obligated to perform during this End Phase, s/he takes such an action. If not, s/he passes. If s/he takes such an action, restart this list. (Such as Veiler wearing off)
5) End the Phase.
https://www.facebook.com/groups/248499755248/10151636913115249/
as seen, turn-player may make an action first, in this case activating yubel's effect so its self-destruct effect will be negated.
also, D-Dasher wrote:
-If you use Effect Veiler's effect on their Lightsworn that has an End Phase mill effect - then during the End Phase they have priority as the turn player to resolve an effect first if they want to.