Safely connecting a relay board to external power supply

A quick question, if we wire the the ground in from the external power supply to the GND on the relay board, and we wire the grounds in off the Arduino harness into the same GND - is that going to cause an issue?

I'm pretty sure I saw something about when isolating your Arduino and Relays that you shouldn't use a common ground....then again, I feel like down is up right now....

Any thoughts or concerns with using a common ground on the relay board for our situation here?

Thanks, eh!