I think since it says "of
your ... movement phase" you can't rapid ingress on turn one.
Page 14 of the Tules Commentary:
Q: If a unit from your army has a rule that allows it to be
set up on the battlefield from Reserves in the first battle
round, can that unit be set up in the Reinforcements
step of your opponent’s Movement phase, using the
Rapid Ingress Stratagem?
A: Yes, unless that rule explicitly states that it applies in
your Movement phase, in which case it is prevented by the
restrictions for out-of-phase rules.