St. Sebastian was a Roman soldier, who, during the persecution of Christians had the idea to convert to Christianity. While this was a spiritually magnificent idea from a Christian point of view, from a Roman point of view it was career limiting: He was promptly sentenced to death. The Romans shot him through with arrows but miraculously this did not kill him and he was allowed to appear before Caesar as proof of divine intervention. The emperor, however, decided to disregard the proof. The Romans then promptly switched to plan B and simply beat him to death.
Post-paganism, the Roman emperor saw fit to build a basilica to his honor. The site chosen for the basilica was the side of a hill where Christians has buried their dead for many years. (Christians buried their dead, Romans cremated them.) The valley next to the hill was filled in and the basilica erected.
The catacombs were primarily used as burial grounds for Christians, with a secondary use as places of celebration on the anniversary of the dead. They were not used as refuge during persecution - although such use may have taken place, this was not routine.
Routine, however, is the photo ban in the catacombs.