Most escorts are just as concerned as you are about protecting their privacy (if not more so). If they out you, then they out themselves as well.

However, the greater your fame the greater the temptation. Tabloids love scandalous stories about actors and musicians, and they'll pay quite a bit of money for such stories about A-listers.

So, I'd say being outed is a low probability, but non-zero risk. In any case, what's done is done. You might consider getting ahead of the story and being frank about your past with your family. Then you can tell them on your terms, on your schedule. And you won't have to worry about being outed anymore.