I don't think you understand. here what ithink happened
You logged into your other account randomly one day through steam.
You accidently went to tf2r somehow without realizing that you were on a different account
If you sign in to one website through steam, you are automatically signed in through other website who have steam login. That is how it works for me anyway, and thats how i got banned from tf2r a long time ago.
tjhat has to be what happened since you say you never went to that website through annother account. TF2r doesn't randomly ban people.