How did Tseng survive the Temple of the Ancients?

[Big D]

To add to what Big D said, if you try talking to Tseng before going further, he will say "I'm still alive". Also, when leaving the Temple, you don't see Tseng at the entrance. Assuming it would take at least quite awhile to get through and back plus with the boss fight(s), it is possible that someone else came and found Tseng.

No, that's before Sephiroth slices him, I haven't a clue what's wrong with him in that scene.

That isn't quite right. The party finds Tseng at the entrance, then later on they are shown a vision of what happened to Tseng. It's a flashback to when he received the injury.