The T4 level is high enough to be certain of the diagnosis, especially with the improvement in clinical signs. It isn't a bad idea to monitor kidney and liver damage and to check for anemia about a week after starting methimazole, though. You might want to ask your vet when he or she likes to do follow-up testing to make sure that there aren't adverse reactions to the Tapazole. Good luck with this. Most cats do very well after treatment for this condition, so hopefully Rusty will stick with the crowd and do the same.
Some cats do require thyroid hormone replacement after treatment for hypothyroidism.
Usually a low dose of l-thyroxine is used on a daily basis in these cases. You might want to check out the Pet Care Forum's Veterinary Hospital area. You might find information there on this problem, as well. I am not sure why this recommendation was made. It is possible your first vet knows something I don't.