My LFS is always selling pairs of these, and the difference in their temperaments can be huge. Some specimens are out and about while others are erratic hiders. The two they currently have are hiders, the female hides so well I have only ever seen it's tail in the 5 months it has been in the shop while the male flails when approached hitting the walls or jumping from the tank. They both act like this despite being at the LFS for 5 months.
I think this is the 3rd pair I have seen for sale there in the last year or so I have been visiting this shop, and the others hid the first week then were out although a bit jumpy.
My experience with them is they hide when first added. My first pair the male hid and never came out. After about a month I found him dead lodged deeper in the rock he liked hiding in. The female hid a lot as well, but would come out to eat at least. She was usually in view after about a month.
My current pair is way better though. Got the female online at about 3.5 maybe 4 inches? She hid for a few days then was active. She is always in view and is much harder to spook than my old female. I had her a month then bought a male at a different LFS. He had been in the shop for about a month, and was very active and didn't mind being observed.
He is about an inch bigger than her, and they squabbled at first with him chasing her mostly. After a day they paired, and there has been no drama since. They patrol the tank close together, and sleep in the same rock it has added a lot to the tank. I was worried it would be a weak pair like a lot of saltwater fish do where they just tolerate each other however they really do seem to get along.
I wouldn't add them last though, they are a cautious fish and mine definitely do not handle aggression from the other fish well at all. When the male anthias is messing with his females he chases them ,and if the triggers are nearby it really scares them. A fish actually coming for them no doubt would keep them hidden all day.
Your tank mates look good in my opinion. I have similar fish with mine, as well as a few types of urchin which they don't bother.