702.23a Phasing is a static ability that modifies the rules of the untap
step. During each player’s untap step,
before the active player untaps his or
her permanents, all phased-in
permanents with phasing that player
controls “phase out.” Simultaneously,
all phased-out permanents that had
phased out under that player’s control
“phase in.”
Rule 702.23a says that phased-out permanents phase in during the untap step of the permanent's controller when it phased out. This means the stolen creature will phase in during my untap step since it phased out under my control.
702.23e Continuous effects that affect a phased-out permanent may expire
while that permanent is phased out. If
so, they will no longer affect that
permanent once it’s phased in. In
particular, effects with “for as long
as” durations that track that
permanent (see rule 611.2b) end when
that permanent phases out because they
can no longer see it.
Rule 702.23e says that continuous effects that affect the permanent continue to expire while the permanent is phased out. When the stolen creature phases in during my untap step, it will no longer be under my control since the controlling effect has already expired. Also, since the delay-triggered effect that would tap the creature if I lost control of it will not trigger since the game never sees me lose control of the creature. It simply phases out under my control and phases in under its original controller's control. Then event of me losing control of the creature never happens.
Instead of phasing out the permanent, if I had used Synod Sanctum or Cold Storage, the creatures would return to play as completely new creatures with no memory of their previous life and would remain under my control permanently. Note that they are still put into their owner's graveyard when they die.
[[Synod Sanctum]] [[Cold Storage]]