Omega vs Mind Control
When Omega is banished it is banished to the owner's side of the field (not the controllers) so when Omega does return to the field, it returns at the owner's Standby Phase and to the owner's field.

According to Yu-Gi-Oh! Official Rulebook Ver 9.1 page 49 and the wiki, when the Omega and a card from your opponent's hand is banished, they're sent to your opponent's (the owner's) Banished Zone. So when it's your opponent's Standby Phase, the effect kicks-off under his/her control.