Phyllis, unless I misunderstand something about your post (and I am not much with computers), what you say does not seem remarkable or unusual, no need to call security.

I have a Mac and use Firefox, and in this respect it must be like other computers and browsers. I log into PayPal. (One should bookmark it -- no need to type it out each time). I am at my home computer. I then go to any other web page, which opens a new window (no more PayPal window open). Then as long as too much time (several minutes or more) has not passed (and I didn't formally LOG OUT of PayPal), I can go back to PayPal (via either my "History" drop down menu or simply using my "back" button) to work PayPal again (that is, I don't have to log in again).

It might be safe to log out of PayPal each time you are finished with it at home, but I don't bother to.

Robert