Some sort of server lag I believe is what's happening.
Recently I got a second character to tier 5 Romulan. I was in ESD for a little bit after completing the claim tier 5 project. I didn't receive the accolade or "Secrets of the Ancients" mission automatically. I decided to go to New Romulus to get some Romulan Marks for projects. I was running through the Staging Area on my way to do the warehouse mission when suddenly I received the tier 5 accolade and mission, at least a half hour after completing the project. I didn't complete any new projects after claiming tier 5. It just took a while for the accolade and mission to be granted.