I think we're discussing two different but similar problems; the two-piece hard vinyl or plastic tire and slicks with separate sidewalls (eg Revell's old style). I used to systematically discard those two piece tires as they were just too hard to make look right, but i HAVE used them a couple of times on "period correct" 1970's kits. never used any type of glue on them, just relied on the wheel interface to hold them. my peeve is the soft rubber tires in Tamiya kits (haven't had Aoshima or Fujimi tires do it) splitting across the tread. matter of fact, tires are one of the reasons i shied away from old-school Monogram kits for so long; theirs never looked "right" to me.
Moebius and Round 2 are the only makers whose tires look good right out of the box. Revell's would be better if they had any sidewall detail to speak of. the '50 Olds and '57 Ford tires are a step in the right direction.