Is moving a units troopers or adjusting cohesion positions, without moving the units leader, considered a move action or would it be a quasi free -1 move, since move actions are based on a unit’s leader?

In order to change a unit's cohesion, you have to have finished a move action. Your unit leader may not have moved from their original location, but that's still considered a speed of any distance up to their speed value. Only after a unit leader has moved, does the rest of a unit establish cohesion. See page 21 and 49 of the reference for limitations and other kinds of moves.

It is a move action, so make sure you place correctly!

On 1/18/2020 at 5:06 PM, TB-79719 said:

Is moving a units troopers or adjusting cohesion positions, without moving the units leader, considered a move action or would it be a quasi free -1 move, since move actions are based on a unit’s leader?

Do you mean as an action on your turn as the controller of the unit, or as a result of some other keyword like Scatter or being displaced?

In order to do that as the controller o the unit, you take a move, then "move" your unit leader no distance, allowing you to move the other models around.

Displace and Scatter both do not count as moves for triggering things like standby though (as far as I know).