Other mistake: Lara pulls herself up to the last step twice as she boards the boat. (00:04:15)
Other mistake: When the submarine surfaces from beneath Lara, from the submarine's angle it looks like the sub is just coming up and will then level out. But we can see the submarine stays at this angle. And in the next shot we can see Lara resting towards the aft rudder. If the submarine would rise at such an angle with the aft rudder just surfacing, basically the complete submarine would be almost out of the water. This angle and Lara's position would only be possible, if she came to rest at the front side of the sub's sail.
Answer: The pressure in the temple would be the same as that of the water just before Lara entered the temple. So no she would not need to decompress before entering at the temple as it was open to the sea, but she would have surely suffered the bends on the rapid accent to the surface.