Your GM is correct
The usage of Psychic Powers is detailed on the core rulebook (page 161):
To use a Psychic Power, a Psyker directs his will into the sea of the immaterium, pulling forth power from the warp to create an effect in realspace. To do this, the Psyker must make a Focus Power Action.
This action is explained a few pages later (page 166):
Focus Time: This entry describes the length of the Focus Power Action required to manifest the power.
On this same page, we have a table listing all psychic powers in the book and what Focus Time they require, which go from Reaction, to Half Action, to Full Action.
Lastly, on the Playing the Game chapter (page 193), we have the following:
Focus Power (Varies)
This Action is used to manifest your Psychic Powers in combat. How long the Focus Power Action takes is dependant on the power being manifested.
So the kind of action you must use depends on the psychic power you want to use.
Under normal circunstances, you are only allowed one Full Action per round, so if you use a Full Action power, you cannot use any other power on the same round.
However, the combat rules state that you cannot make the same Half Action twice in the same round (page 188), which limits you from using your Psychic Powers (by using the Focus Power Action) to once per round:
Note that you may not take the same Half Action twice.
Always agree with your GM (even if you actually don't)
Even if he was wrong, you shouldn't attempt to prove him wrong, that is disruptive to the game. Just point him to the rule outside of the game, and accept his judgement.