If Tyler is Voq, then explain the fight scene between him and L'Rell.
Which, I might point out, had no witnesses.
1) Tyler set up the time and place of their escape and his collapse on the floor in that location and said he was too weak to go on, knowing Captain Loco would return for him there. Notice how he suddenly got all his strength back to attack LL'RellJ? Could be anger-fueled adrenaline, could be a bit of pre-established theater to sell his story.
2) Lo'relai Killmore gave Tyler a distinct head nod before he attacked her signalling that he knew what to do.
3) The fight was actually witnessed both by a Klingon warrior (though he got green-misted) and Lorca, who walked in on the end of it when the tables had turned and stopped it by shooting off half of L'Oréal's face. But she can just put some concealer on it and it'll be fine.
4) Then L'Orca jumped out of hangar bay with Tyler and they were Free Willy, pursued by the worst shooting Klingon ships ever. These were the Stormtroopers of ships. Except like the time the Stormtroopers wanted Han, Leia, Chewie, and Luke to escape the Death Star alive and lead them back to the Rebel Base (or Discovery in this case), they weren't actually trying to kill them.
Or, like the others said, Tyler is brainwashed and doesn't know who he really is.
But the whole "Choose Your Pain" game seemed engineered as a trust building exercise and means of easy escape by putting armed guards in fist-fighting range. Plus, the fact that Tyler lied about his situation with L'Rell and was suspiciously unmarked until he needed to gain Lorca's trust, and that he waited for Lorca to arrive to make his move, leads me to think he might still be conscious of who the Voq he is. The dialogue between Tyler, Cadet Twitchy, and Michael BurningMan in the clip from the next episode also makes me think he might still know who he is.