Those cars, like others of that era, had "bowl vent valves" which vented the float bowl to the atmosphere, as a normal situation, when the throttle is closed. Replacement carbs have the nipple to connect the bolw vent to a carbon cannister (as latre models had). It might not be boiling fuel into the throttle bores per se, but you will smell the evaporated fuel.
When re-starting, use about 2/3 throttle openning rather than otherwise. This way, the accumulated vapors will clear out sooner, which should mean a bit quicker start. Just the nature of Chrysler B/RB engines, back then. Similar GM or Ford vehicles didn't have those issues, though. Not quite sure why . . . Although Buicks with their "accel pedal start" kind of got around that issue as to engage the starter, the accel pedal had to be at WOT, which stopped being used in the earlier 1960s.
Any modern gasoline is quite a bit more volatile than even the winter blend fuels for when the cars were new. Which also means "easier to evaporate".
Enjoy!
CBODY67