Tennessee and Alabama are tracking each other closely in new COVID-19 cases. See the graph below. Apart from a spike in daily cases at the beginning of May due to an outbreak of the virus at a prison in Tennessee, the number of new daily cases have been close.
Although this makes it appear the virus is continuing to spread, when you look at the daily number of active cases, which accounts for recoveries, the statistics in Tennessee appear more optimistic. See the graph below. Alabama is one of 14 states that does not track recoveries, so I do not have the statistics to track active cases in that state.
Apart from a sizable net increase on May 12, the number of active cases is staying relative constant, with almost as many people recovering from the disease recently as the number of new infections. This, along with Tennessee’s significant amount of testing, provide confidence that the re-opening of the state may be sustainable.