I'm not sure how you think this works, but the phone company doesn't know only the one tower you are currently connected to. Your phone regularly senses the signal strengths to all towers in range, and sends the list of strengths to its current tower. This allows the system to decide when to tell the phone to transfer to another tower. In the city, the microcells (and smaller) are also really tiny. Until about 2000, the phone companies were still thinking (or at least claiming publicly) this data alone would be enough to meet the U.S. FCC 911-emergency requirement to locate 67% of phones to within 50m. In the end, they couldn't quite do it (mainly terrain and canyon effects), but it was close. Eventually, it got cheap enough to put GPS in the phones that they just gave in and used that.
How much of this extra information is actually recorded isn't published, although it's probably thrown away mostly. (The algorithms for predicting when to transfer a phone to which tower are trade secrets.) If they wanted to track you, certainly down to which highway exit you are at, the information is available. This tracking reduces the number of towers required along highways, which saves money, which motivates research.
Even if they knew to within only a mile or two, my original point would be the same. Obviously they know which tower to send the ring message to, so they have a general idea where you are. Is tracking a person's movements to within a mile fundamentally different to tracking them to within 10m?