Well, the actual order of events are always up to the characters, but I believe the plan is for the group traveling there to rest up and restock on supplies, and for them to receive the information they were going there for in the first place in regards to how a person recovered from the Withering. They will probably receive the information immediately upon arriving (that is one of the tasks given to the representative meant to meet them), but what happens after that is at the mercy of free will. I suspect that they will either take a day or so to recuperate right away, postponing everything until they are all at least somewhat healthy again, or they might want to seek out the survivor of the Withering themselves to ask their own questions and get their own answers. Eventually they will most likely go to investigate exactly how the recovery occurred, though, and continue their quest to end the Withering.