BFF's first album was in 1993, and Jamiroquai was formed in 1992, I think. Both of those were well after the term was muddied beyond recognition. I'm skeptical of the claim that Jamiroquai was being tagged "alternative", same with Cherry Poppin' Daddies (also 90s, IIRC).

Note that by the mid-90s, if not sooner, a lot of 80s alt-rock was seeping into AOR / classic rock / hard rock playlists. (Source: was a DJ on a classic rock station from 1995 through 1998. Played R.E.M., Pearl Jam, bunch of other alternative/grunge stuff alongside 60s/70s/80s classic rock. And a little bit that wasn't technically on the approved list since I was usually working midnight to 6 a.m., but that's another story.)