Antalya airport transfer to town centre after midnight: public transportation

In two weeks I'll be arriving by plane in Antalya airport shortly after midnight. I then have a stay of 10 hours before I need to be back at the airport for another flight. I'm travelling on low budget, so cheap hotels/accommodation and public transportation is the way to go. I haven't found really cheap accommodation very close to the airport, so I will go to the town centre where I've found some options.

Is my assumption correct that there is a regular Havas bus from AYT (domestic terminal) to the town centre also after midnight? (For the way back to the airport in the morning I'll take the tram which seems to be the most comfortable way.)