After tweaking my Contacts-- basically making sure that there was a unique entry that had a specified email address on both devices-- I now set Air Drop for Contacts Only. In that way, you actually do restrict it, at least to people in your Contacts list-- if they are around. I basically just use it for our family devices.
We're now using an iPad Air 2 (iOS 9), iPod Touch 6, (iOS 10) and MacBook Air (El Capitan).
I did find that I had to permit sharingd in security panel on the Mac to get Air Drop to work with it. To your question, I'm getting the prompt sometimes, sometimes not and then the file transfers automatically.
Let me go try this now for you and see if there is pattern!
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OK! Here's what I'm seeing. Between i-devices, it sends the document and THEN prompts you as to which app you'd like to open it in. (Doesn't make sense, does it?! It should ask first.). From the Mac TO an i-device, you also get the prompt.
However, from an i-device TO the Mac, it simply transfers it into the Download folder! No prompt at all. Now, that could be because I've asked Pages to convert the document to Word, but that is something else I'll have to try.
I do NOT know of any setting that controls the prompting-- none or always-- perhaps, the Everyone setting does it. Maybe someone who really know AD will chime in.
I'd just as soon get a prompt, just in case it's someone I don't know trying to send something (maybe I selected "Everyone" by mistake) and also to be sure that AD is working! Otherwise, when I transfer something TO the Mac, I'm not sure it worked! The downloads folder icon in the dock does sometimes bounce, but with a small file, that seems to happen in an instant and is easily missed!
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I do wish that the Air Drop button would not always say "receiving" on it on the IPT. After all, I'm typically sending not receiving!
I hope all that helped! If you figure anything out, let us all know!