I have said what I have said and - as have koraks and Railroader - explained precisely why the nonsense propagated through various Arduino topics is entirely misleading. Again, the on-board regulator is essentially only for demonstration use of the bare board if nothing else is to be "powered".
Good. Cross-posting is a nuisance as different people may end up helping with matching advice on two versions of the same project and the duplication just wastes their efforts.
Essentially any "buck" converter unless specifically and deliberately isolated, has the same ground on input and output. But it is important to run the 12 V input and ground together from the 12 V power supply, and the output 5 V and ground together from the converter to the parts requiring 5 V.
In particular, you must run 5 V and ground together from the converter to "JD-VCC" and "GND" on the relay board with the link removed, and 5 V and ground together but separately from the converter to the Arduino and then connect your control outputs from the Arduino together as a bundle with the 5 V from the Arduino to the "IN" pins and "VCC" on the relay module.