I'd be interested in what you find... so far I have not encountered this bug at all and have been running 100 tick speed almost all the time for a few weeks and I haven't triggered this bug.
Yeah, I'm not entirely certain that it is the tick speed, just that I've had the tick speed cause an issue when unlocking Zeus for the first time. It caused a menu glitch and I couldn't collect the loot for the tutorial to get the AP to buy the first piece of gear. That's the only reason I'm thinking tick speed.
It could have been something else that caused the issue for me. I don't remember there being a new menu popup, just the missions start tracking towards unlocking the relics and earning fragments. Which neither were working for me.
Any mission, including farm ones. Make sure you have F1-1 maxed and, later, F2-1. Other missions also count and you should be allocating staff to them too, but F1-1 and F2-1 are priority.