If at any time the puzzles are not thier, then just wipe to refresh the instance. This is a bug that is caused by the game checking multiple players instances if players are on different steps for quest, or have quest done. It also helps if the first person to enter the sector where the puzzle is, is the person that is on said quest step for said puzzle. Also if the step is not progressing for you, then try to do the puzzle yourself, and collect the reward, also do all the puzzles in one session, and that will force the triumph checked off, do then all you have to do is claim the triumph inorder to get into final puzzle room. Also EVERYONE in the fireteam has to have that triumph claimed, if one person does not, then that barrier remains up. If you join someone who is already in the room, to try and cheese it, then the barrier goes up and gives the person inside a turn back which results in thier death, however if they are fast enough they can finish the puzzle, before the turn back kills them, thus giving everyone who is loaded in, and close to the sector registration zone, the catalyst completion.