Excellent question with a subtle answer. As others have commented, "They seemed to have a good time," sounds correct. It sounds correct because in some instances it is. In your example it is not the best answer.
Seemed is merely the past tense of seem and 'seem' involves YOU having interacted with it in the present moment, even though that present moment may have occurred in the past. "They seemed to have a good time," implies that something happened in the past that you witnessed. "They seemed," means you saw it when it happened, in the past, and now you are reporting back what you saw.
In your sentence you did not witness Tim on his trip. You are instead, at this future point, making a judgement on what happened in the past. You have no experience of Tim's camping trip that occurred in the present, therefore the simple past doesn't work as well. You express your lack of presence during the event by using "seemed to have had" meaning the information you are using to make this determination was all provided after the event occurred.