You sure you had it turned off before? As handoff has been around for years now.
Definitely had it turned off as I haven't ever seen this happen before where when someone accesses a website on my iPad (usually the kids) I get the Siri Suggestion on my iphone.
As soon as I updated to beta 7 I noticed this. Had my wife and I n it been on the devices in the same room at the same time I wouldn't have realised. She told me what site she was on and as soon as clicked the open new tab on safari on my phone, I saw the Siri Suggestion.
I've always had the Handoff setting on, and I've always seen various suggestions between devices. If you definitely had it turned off before, then maybe it was like the issue where people's bluetooth got turned on when a new iOS update installed a couple years ago.
It's only devices using the same AppleID, I think?