Theres no exact proof. We just see them standing there as the PD collapses. They probably got sent to the end of time, and went to their time. But when they arrive there, the time crash probably happened, otherwise that screws up so many things anyway.
Why would they arrive at the end of time? Why not at the point where they entired the pocket dimension?
They would arrive at the End of Time because they were only 3 and they had to brought back the 4 other time travelers who were waiting there while the others fought Lavos.
You fight Lavos with 3 people. Lavos is killed, and still, only 3 people fought him. If 4 or more were there, sure, maybe they would end up in the end of time. But there was 3.
You misunderstood. I'm saying that 3 persons fought Lavos while the 4 other time-travelers were waiting for them at the End of Time. It means that after the battle, there are 2 scenarios possible:
-Either the 3 fighters go back to the End of Time to meet with the 4 others, then they all go back to 1,000 AD for the Moonlight Parade,
or
-The 3 fighters go directly to 1,000 AD from wherever they were, and the 4 others go to 1,000 AD from the End of Time. The 2 groups then only meet at the Moonlight Parade.
In my previous post I assumed that the first scenario happened, because it makes more sense. The second scenario doesn't make sense because after such a battle the 3 fighters would want to rejoin the 4 other as quickly as possible, and probably thank Gaspar too. Moreover, this second scenario would be quite complicated timeline-wise (the 3 fighters go to Keystone T-1's 1,000 AD while the 4 others would go to Keystone T-2's 1,000 AD...).