When I do a "sketching session" with my artists we establish THREE things- and these are ETCHED IN STONE before the artist leaves this session!!: Tempo, Key, and Feel! I'm very up front with my artists about this! I enforce to them that once they leave, and I start production, these things will NOT change!
The way I typically get the 'feel' is I drop in a drum track that "feels like the song". I'm a musician for a bunch of years and this is one thing I believe I do well. I get them to play along. (Usually, I tap tempo as they begin playing so I know about where the tempo is before I drop in the drum loop). I'll stop after the first chorus or so and ask them "how does it feel." Frankly, most of the time I'm very close to the tempo. Once we get VERY close we cut a bit of the song. I play it back and ask them about the tempo. If they say "It's good" I'll ask "if there's any way you'd go with the tempo- up a couple BPM or down, which way?" By this time we're pretty much on it. We cut the song, I play it back and ask AGAIN "how does it feel to you?" If they say "I'm good" then I tell them again, "the tempo, key, and this feel isn't going to change, are you good with it?" They either have to say yes or no (and we'd start again) but almost always, it's yes. They split and my gig starts. They come back for a vocal after I'm done producing the track.
So far, after 12 years of producing- full-time, and about 1000 songs, I've yet to have someone to complain! I guess every producer has a process and this is mine. It works. ...thought I'd share it to save you some grief down the road. ...and by the way, I'm pretty much an old-school cat myself.