For me the problem is that Kirk never gives any order to bring the ship around. Spock's last "location" is a bearing
. That "location" was "holding steady" which would indicate the bearing never changed when the Enterprise fired the torpedo. I'm not saying it's impossible for the Enterprise to turn, just that there isn't enough information to confirm that she did turn (like an order, a visual fx, new bearing).
SPOCK: Unknown, Captain. Nothing within sensor range. Something now, Captain. Very small. Bearing one two three degrees, mark one eight. Range ninety thousand kilometers.
KIRK: That's our target, Mister Sulu. Prepare photon torpedo.
SCOTT: Shields still holding, sir, but the drain on the engines is reaching the critical point. Ach, we lost warp maneuvering power. Switching to impulse.
SULU: Photon torpedoes armed, sir.
KIRK: Has the target changed location, Mister Spock?
SPOCK: No, sir. Holding steady.
KIRK: Ready photon torpedo number two, Mister Sulu.
SULU: Ready, sir.