Something is awfully wrong.
Paper do not turn all black even in not-so-dark darkrooms. For example, my "darkroom" used to be a temporary setup and it was "dark" to a point I could clearly see my hands after I get used to the darkness. My paper completely stayed white.
So I'm guessing either your paper is fogged or your safe light isn't safe at all.
Turn EVERYTHING off, and at night, in your "darkroom", just develop your unexposed paper, then fix. If you have fogged paper, it will be something other than white. If it turns black, then it's totally toast.