We went last year and DS is allergic to nuts. I knew going it that we could let the server know when we were seated about his allergy and they would relay the info to the chefs (as TS restaurants). Most of the time we would speak to a chef before they prepared DS's meal.
What I didn't know was that we could have the allergy noted on our reservations. One of the hostesses mentioned the allergy when we checked in, which shocked me. Apparently it was noted on at least one reservation, but not all. She suggested I stop at front desk/guest services at the resort and have them add it to all ADRs. We did, and they updated the ADRs. This alerted the restaurants before we got there. As I mentioned before, we spoke with chefs at most, if not all, of the TS restaurants. DS's meals were prepared without & away from nuts, and all went well.
One other note - we ate at a few buffets, and we even spoke with someone there about the allergy and which foods to avoid. There were plenty of options available for DS, but I am pretty sure they would have prepared something else if there was not enough there for him to eat safely.
Good luck!