Essentially, Revan gives 1 ally the "intuition" ability every round after initiative is rolled. Revan, Ulic and Basilisk is 200 points. Can the basilisk attack enemies when Revan chooses it before a round begins to move up to speed? Strafe reads thus...,

Some characters with Flight also have Strafe Attack. This character can move up to double speed and attack each enemy whose space it enters instead of using the targeting rules. Roll each attack just before this character enters that enemy’s space. This character cannot attack any enemy twice in the same turn using Strafe Attack, and it cannot move directly back into a space it has just left. A character with Strafe Attack can still make a normal attack on the turn it moves, as long as it moves its speed or less. Prior to using Strafe Attack, this character must designate a legal space to end its move in. Other characters cannot enter this space while this character is using Strafe Attack.

My thought was this, if Strafe does not replace attacks, does not replace turn, does it grant the "strafer" indiscriminate advantage of being able to attack anything it moves over regardless? If so than any CE that grants extra movement would allow the basilisk to attack outside of its turn? So yeah, better rephrase, does Revan's commander effect allow strafers to attack outside their turn if the strafers happen to move over enemies?

Strafe Attack can only be used on a character's own turn. This is covered in the errata.