I don't know about DTAC, but on my AIS phone, when I buy a roaming package, I can choose the start time. it will be in Thai time.
So I normally get it to start the same time my plane is due to land. So if I landed UK at midday, accounting for time difference I would choose 5am Thai time.
You may have to switch your phone off, then on again to activate any roaming package, but if you have the DTAC app, I am pretty sure you can check it there.
Mine normally starts automatically.
Bear in mind you can use apps such as WhatsApp, FaceTime, Telegram and Skype to make free calls over wifi to keep costs down. Though they will use data if not on wifi.