My handoff is off as well. Always has been.It's not Siri but Handoff. You can disable handoff and it won't show up but you disable all handoff features.
I know what it is and I want it off because it’s not useful to me and is probably just using unnecessary resources and battery. And it was showing up only when I was viewing the weather channels maps. Never showed up in iOS 10 and this started right after the update. Just a weird bug I’m thinking.It says that you recently searched for that in Safari. So it checks if you want directions to that location. Guess there isn’t a setting for that particularly feature.
What’s located at the bottom is more than just handoff. It’s app suggestions based on time and locations and also apparently smart suggestions based on what you are currently doing. Never had that happen to me (I wish it did).