While I like the idea of Kiln time traveling the slow way, I think the fast way makes more sense. One of the key parts of the relic is they are searching for a way back home. And while time travel obviously exists in modern times, it feels kinda roundabout. Also, that would eliminate the need for Kiln to be protecting their ancient tech/looking for more of it was simply a healing pod that was now just a reminder of home, Vs it being their only reliable way to get back home.
So the pod did cause them travel through time the fast way, though how is unknown.