Can people privately follow me on Twitter?

[...]

I have two Twitter accounts, one for personal & one for business.
I follow almost the same list of people from both accounts.
On occasion, I also Tweet people who I do not follow.

On one profile, I found my other profile on the "suggestions" column.
It says it is being followed by said people that I do not follow. I checked this at certain times of the day to make sure it wasn't an error.
I am also apparently being followed by a big fan of one of them, who also isn't on the list.

When I go back to the profile where they are said to be following me, they are not in my list of followers.
I have not tried to DM them yet, because I don't want to for now, in question that they might stop following me.

So are people following me privately on Twitter? Or is Twitter is trying to get me to following myself by lying about they're following one of my profiles? The fan account would explain it's legit, but I'd like to be sure.

[Jill]

You would need to go directly to their Twitter page and look to see if they are actually following you. Your twitter list of followers might not be updated. Just go to their page as this is most accurate.