The oil cooler lines attach to the sandwich adapter. The stock motor has a sandwich adapter that the oil filter screws onto. (I don't think the stock adapter has a thermostat, though, correct me if I'm wrong.)
Since the stock oil cooler is "immersion type" -- coolant on its way out of the radiator is supposed to cool the oil -- it's not really much of an oil cooler. People run these things with that arrangement though. Where I live it routinely hits triple digits in the summer, and "immersion" coolers aren't worth a whole lot. So I may be a little obsessed on this topic.
However, the turbo shaft bearing is oiled with a dedicated line that leaves the block immediately after oil from the filter enters the block. Keeping that bearing supplied with good oil is very important. That's all I know.
As they say on computer-related forums, "Hope this helps." (When they say that, it never does.)
--Jim Howard