After deplaning, everyone boarded buses which took us to the "Arrival" tent. There was a separate line for "Transit" that passes through immigration. As our (Delta) plane was the only one at that time, there was no wait. The only transit desk (SBC in our case) we experienced was on the other side of the immigration stations and in the baggage area. Once SBC had enough passengers for a flight, they escorted our group from the Arrival tent to the Departure tent through a door marked "Transit". I don't recall going through any security screening as a transit passenger. From landing to departure the whole process took maybe 45min and we arrived at SBH an hour early.
I would imagine that the amount of hassle is directly dependent on the timing of the incoming flights. Shortly after us, a (late) Spirit and (on-time) Jet Blue flight arrived. We overheard the SBC folks excitedly discussing that they had to get our group in the air before the next batch of passengers. Could be coincidental, but all the US planes I saw were smaller 737's possibly reflecting reduced demand.