What is the best time to add a new fish to the tank?

Everytime I add a new fish to my tank, the other tenants surround it and
show some territorial behavior, especially my dear damsells. This cause
stress to the new fish. My questions is, if you add the fish with the
lights out, would it make a difference in the morning?

Less traumatic perhaps?

I ask because I added a lawnmower blenny and he got chase even from the
yellow tang, and still being bother by the blue tang and of course my
damsell. By the way, the damsell have a particular behavior when bullying,
he shake his tail on the face of the other fish, why is that?

At the same time I put a tunnel digger goby, 2 days later he was dead with
blood stains on one side (inside), which suggested me he might have eaten a
crab and got cut inside.

I'm planning to add either a tiny yellow goby (I'm still considering due to
the damsell) or a coral beauty which seems more safe to the coral than the
butterflies.

Daytime or Nightime, that is the question?

TIA

Ruben