Is this still an issue? I am going to test myself, but this was one of our main reasons for looking into using Amplify so disappointed to find that it does not detect this situation. It's an issue with all Safari versions, desktop as well, that with private browsing turned on, the local and session storage gets a storage limit of 0 bytes, and thus throws errors when you try to put anything into it. So what we need is for Amplify to be doing a quick check to see if it can save something in storage prior to using it as the default.
Mary Jo