Excited am I = unusual word order. The guy was trying to be clever. "So did I" = standard response which mean you did the same thing.

I am excited is the correct word order. Example: [ A] I am excited being on this plane. [B] So am I.

this named in english questions tags . when you say something and you want comfirm what u said you use it. an examepel i'm lazy . if i want comfirm it i say .amn't i or aren't i. but if the santence was in nigative we say an exampel : i'm not lazy to comfirme my speech i say am i.are u ect..... but in santences verb like i study evry day .when we want comfirm we say don't i. you study don't you ect........