Water can travel quite a distance through cracks in caulking on roofing and walls by capillary action. A leak test would be a good thing to do at this point. Even if you find suspect caulking, there could be other spots that need re-caulking too. You can rig up something to do a leak test yourself or can get someone to do it for you. TTs are somewhat "high maintenance" and things like regular inspections of caulking can't be ignored but too many owners do.
Is the water heater nearby? Or a leaking window? I'd think there'd have to be quite a leak for it to rot out that badly in just a few years.
TTs can be somewhat easily de-constructed as far as cabinetry, seating, etc. goes due to the way they are built. The floor could be more of a challenge though, especially if the rot goes under the exterior wall. If the underbelly is not enclosed, that will help. All you can do is keep pulling rotted and damaged wood out until you get to undamaged material.
Some photos could really help for folks to comment on.
