even if kate was only in martin's house for 1 day, it's still creepy and not a good look for martin. he's a grown man who let a female student spend the night in his home without notifying her family or the authorities that she was there. furthermore, he's already lied to kate's mom. she came to the school and expressed concern that her daughter was missing, he acted like he didn't know where she was even though he did. it totally makes sense why he would panic when he saw the tape, even though kate hadn't been at his house for very long at that point. i hope you finish this season. there's only a couple of episodes left and the mysteries and questions do get answered by the end.