Yes, that is correct Nicola, from what I saw last night at Dalaman. The Turkish Airline flight landed at domestic early at 19.33, the Havas buses for fethiye and Marmaris arrived at International at 19.54, and waited until 20.15. There is a large board at the International terminal from Havas saying they do the departures for Turkish Airline and Pegasus flights, and also arrivals, collecting first at domestic and then going to International and waiting for a few minutes. I asked the man taking payment in the car park office about the Muttas bus, he said they only do departures, not arrivals. I do not know if he meant at both the Domestic and International terminals.
I do not see how 'it suggests someone has made some seriously wrong life choices' if they choose to take the Havas bus rather than pay for a private transfer.