Time Machine only backs up when all users are logged in

I am having an issue with Time Machine because it will not back up unless I am logged into both admin accounts on my computer. Is there a way around this? I only created the other admin account because I needed to change my root folder library name so it doesn't need to stay an admin account if that is what is causing it. I just don't understand why it needs to be logged into both accounts to backup. There is no data or files on my secondary admin account so it shouldn't need to back anything up there I only want it to backup my main account.