Mackanstein's page

"Move your Speed" is a specific action p. 247

Many nonstandard modes of movement are also covered under this action, including burrowing (using your natural burrow speed, if you have one), climbing and swimming (using either the Athletics skill or your natural climb or swim speed, if you have one), or flying (using the Acrobatics skill if you have either access to flight or a natural fly speed).

So yes, you can use jump jets as part of your trick attack action.

That would work if it wasn't for the fact that jump jets are not just a nonstandard form of movement, they also require activation via a move action.

You can activate jump jets as part of a move action in order to fly during your movement.

Trick Attack requires a full action.

As a full action, you can move up to your speed. Whether or not you moved, you can then make an attack with a melee weapon with the operative special property or with any small arm.

And a full action cannot be used RAW in conjunction with a move action. They're a seperate type of action altogether.

If you take a full action, you can’t take your usual standard, move, and swift actions.

While I personally would allow my players to use jump jets as part of a Trick Attack at the table, I really don't think it's RAW.

I'd say your suspicion is correct. Trick Attack is a full action that allows for an attack preceded by optional movement up to your speed, not an actual move action. A GM may allow it, of course, but by RAW it's a no.