@Robert ******
I don't know where you got your info, but for expired passports you normally have to use the old passport for the visa and the new passport for entering and exiting the country.
Immigration cannot transfer a visa.
They only can tranfer stamps of extension, and that is meaningless for DTV, because you normally don't extend a stay on DTV, and just will get a new stamp in your new passport when you enter the country again.
At that moment they might ask to see your old passport because that is connected to the visa.
They also might just stamp the new passport without asking for the old one, but that is not a guarantee.