It may or may not be from St. John, you could possibly be pulling lte from Stt. If you have direct line of sight to the tower you can still get service. If you get to redhook and you still have lte then it could be from St. john but if your lte goes away then you were pulling lte from a tower on st thomas. From cruze bay st john you actually have direct line of sight to at least 3 or 4 towers on st thomas and could easily get lte service from one of those towers if they are broadcasting an lte signal.
EDIT: To add, from redhook, you will have direct line of sight to the tower in st john if you don't have lte in redhook then that tower in st john isn't the tower your phone connected to for lte.