Laguna and company did not die on the past on the excavation site because our heros heal were transferred to them.
They recover and when they are fully recovered our heros were on the prision and their consciousness were sent to the past.They recover their health.Squall is therefore alive.

This is also what happens with Propagators .
When one dies,another one with the same color gets inside the dead one transferring their health.Of course,there is a third one who has the ability to transfer the consciousness.