Does an effect caused by an objective belong to a player? There are three possible interpretations. One is the second player as it is part of their fleet. The other interpretation is that is the player who is being instructed to do something by the objective. Third is that the effect belongs to no one.

The specific example is the timing of Hyeprspace Assault and Grav Shift Reroute.

Grav Shift Reroute: Before deploying fleets, place 1 grav shift token anywhere in the play area...

Hyperspace Assault: Before deploying fleets, the second player sets aside...

This is the relevant line from the rules reference:

If both players have effects with the same timing, the first player resolves all of his effects with that timing first.

I think most likely the objective card is an effect that belongs to player two, but I could see there being different interpretations.

What other way would you determine it...

What "First Player" Does is the purview by the First Player.

What "Second Player" Does, is the purview of the Second Player.

The only other way you could interpret it, is that the Objective Card itself belongs to Player 2, and thus, they own all of the effects, and would determine timing...

But you could also argue that they own 1st player effects, and can determine when they do things - which goes against the spirit of the "first player first".

So I don't think objectives belong to anyone, but they do provide an effect to the second player in your example. Therefore, the rule you quoted would mean player 1 does GravShift, and it followed by player 2 placing the tokens. I can't think of another example off the top of my head, but an effect does not need to belong to someone, even though that's how nearly all of them are. I think the key thing is who it is targetting and the ownership of that.

I would say player 2 could decide in this case since they both happen at the same time before fleets are deployed.

Mainly because player 2 has that advantage since he has to go 2nd once play begins

When timing is simultaneous:

1st player goes 1st

2nd player goes 2nd