This may have been answered elsewhere, or it may just be as straightforward as it says on the card, but..

My friend and I had a game last weekend and I was flying a Tie/D with Ion cannon, I shot at a ship with my Ion cannon and hit it for its last hull point.

The title says that I can perform a primary weapon attack after the attack with the equipped cannon, I assumed I could shoot again at a different target, however my friend said the attack must be against the same target.

Who is correct?

You are correct. It says you "may perform a primary weapon attack." There is no target restriction on this card. See also Gunner crew.

If you look at the Timing Chart for Performing an Attack, it tells you to return to Step 1 where you can declare a new target to attack.