Okay, good, I’m glad it wasn’t too tech unsavvy! I just did a super quick search and Apple does say that Safari blocks cross site tracking but what you’re describing seems like something different.
Well basically my NoScript warned me of the cross sight issue. But it couldn’t prevent it. So if Safari actually prevents it then that might help. But I wouldn’t put trust in it. I would clear your cache before logging into sensitive systems like banks, Etc.