As you moved out of range of one tower, would the operator transfer the call for you? Or was this strictly (in the case of driving on the highway) for short calls? Did you always have to know where your driver would be, to locate the tower to use, or did they have some method of "pinging" to determine where a receiver was?
It's remarkable how well modern phones handle the "hand off" process between cell towers at 70 mph!
Based on my video and the more refined specs in Halcyon's video, it looks like the transmission you receive comes from a really strong central transmitter, so, that direction and receiving call notifications covers 1 +1/2 city wide. It is the short distance which the car's transmit to multiple receive antennas operation. Considering that those antennas might have private wiring to the transmitter station to coalesce the call onto a regular phone line, auto selecting between the not strongest, but strong enough for clarity of the 2 adjacent received signal on that 1 frequency is something analog tube electronics with the added hard wiring to the central transmitter antenna can handle.
Remember, we are only talking about 33 channels (if I remember from the video correctly), which was then increased to 150.
(EDIT, in 1940's there were 21 channels, in 1950's, it was increased to 33 channels. If they had better crystals and narrow band IF saw filters in the 1950s with a narrow band FM audio, there would have been enough room for tons of channels in the newly allocated 450MHz band. But to handle the flood of calls there, only going PLL tuning and MCU computer code could create an effective phone on such a crowded network.)