Why is втомлений not used here? To me, втомився sounds like he "tired himself out" because of the suffix ся.
I'd say, "Він дуже втомлений" is indeed "He is very tired", this translation is better. "Він дуже втомився" has a verb, not an adjective there, so it's more like "He got very tired".
But if we don't pick on details, as a flexible, not word-to-word translation both could work.