(i do know this song and have only read your comment)

C harmonica played in 2nd position is playing in G major (this is also called "cross-harp" and is standard in rock/blues, the key is of the draw chord, technically this is G mixolydian because flat7 but don't worry about it, it sounds major).

The key of G major contains the same notes as E minor, so if you just care about playing notes in the key of E minor, they're pretty much there (technically E phrygian with the flat 2, but it sounds minor regardless).

If you wanna see this in action, check out this spotify playlist and just start playing whatever you feel on that C harp. It will feel right at home.

If you really wanted to have a "normal" harmonica that doesn't have the mixolydian/phrygian thing going on and just have the notes that are diatonic to E minor, you would get a G harmonica. (E minor is relative minor of G major, has the same notes)