Nashville is only about 80 miles from the TN/AL line. Pulaski and Fayetteville. It's 82 miles from Columbia, TN to Decatur, AL but Columbia is a little off the interstate. So either they had their phones off for a whole and turned them on again or they were around in other areas.
If you left Columbia and drove the quickest way, you would be in Decatur in and hour and 15 minutes at the most.
Crossing the state line, you come to Madison and Huntsville, AL just a few miles over the line. Both are very large, especially Huntsville and they could have gone to Walmart or various other stores.
In both areas they wouldn't have stuck out really. Redstone Arsenal and NASA are both in the area and there are a lot of transplants that come and go from the military and government contractors in the area. Strangers wouldn't be put of place in either area as much as they would be in Decatur.
Decatur is bigger than you might be imagining. There are two high schools. Lots of strangers. And large employers that have many temporary employees (engineers, mostly). It is not a city where everyone knows everyone.