Having a PCR positive doesn’t mean one has active Covid19, which is the disease.
It means you’ve been exposed to Covid-19 and people shed dead virus (non-contagious) for up to 12 weeks after infection, which can trigger a positive test.
They tested everyone before classes started and only 249 tested positive at that time. The 1000 new positives are from new infections over the last two weeks.

Early COVID-19 test results for Alabama college students show low positivity rate
The first 30,000 coronavirus test results for college students in the state of Alabama are complete and results are in.