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To me he doesnt seem to be showing any signs of stress such as poor color or spots. Is he eating well? If so, I would just watch him. You might want to post this over in the disease sections. I have never heard of a disease that causes the tips of the fins to turn black like that. On the other hand, I have never seen a Bartlets anthias w/ black tipped fins either.
I wouldnt worry about him then. That is usually one of the first things to go when there is a problem. He may be just a slightly different breed. It sounds odd, but its not uncommon. For example...the Fox face. Everyone knows what the common one looks like. The less common one has a black spot on his upper flank.
I think your anthias looks pretty cool like that! Maybe his mom cross bred w/ a black tipped shark!