피곤하다(adj) is a little like the emotion words (기쁘다, 아쉽다, etc) which have distinct usages depending on the person. Because they represent something only the speaker can know directly, we use the adjective for oneself (나는 기쁘다), and the verb (친구는 아주 기뻐했다) for the second and third person. The verb's -해하다 ending focuses more on the reaction of the person, not the state itself as does the adjective. So in your example, 세민 씨가 어제는 피곤해하더니 is natural but 세민 씨가 어제는 피곤했더니 is not. -더니 is a verb ending showing how some new event or state contrasts with an earlier one. The key thing is that it always indicates something in the past ('더' has this function), so 피곤하더니 is almost never made into an explicit past form. What's tricky, though, is that -더니 is sometimes used in the past form when it involves an action verb, to indicate the "completion" of the action (as distinguished from a time point in the past). This is a very subtle and difficult concept, but here's an example. 1. 머리를 쓰다듬어 줬더니 강아지가 너무 좋아했다. (줬더니 indicates a completed intentional action). 2. 아이들이 아까는 잘 놀더니 지금은 싸우고 있다. (놀더니 means the kids were playing together (ongoing state in the past) when the speaker saw them, which has now completely changed). Both 쓰다듬어 주다 and 놀다 are action verbs, but #1 is talking about a committed action (typically by the speaker) and the ensuing reaction, while #2 is about a state (of the children playing without fighting). If you change the tense in either, the sentence will sound strange.

It is because the person who was tired is not the speaker. Even if the speaker was tired, we may say ‘제가 어제 피곤했지만 오늘은 괜찮아요.’ not 피곤 했더니. However .....해 하더니 is not used as describing the speaker’s status. It is for 2nd or 3rd person