Hmm I never felt that it had to be missions I accepted, and that shares helped.
Also, its definitely not 10. First, there appears to be some weighting. If you do lower-tier missions, it takes more. If you do higher tier (via shares) it seems to take less. It almost feels like its based on the xp you get from the missions, like Kill+Stash makes it go faster.
But that's also not entirely correct. I made a test quest that lets you turn in 1 grass to Trader for 100,000 xp, and is T1. Assigning to myself with console, I got past first couple tiers in only a couple turn-ins. I think it was 2 to get to T2. But it took like 20 to get from T4 to T5 (this was about 2 months back, i don't recall exact number).
Anyway, the logic seems squishy, not hard, when getting between tiers. If you're doing 100% of your questing together, it does seem weird that they advanced and you didn't. Keep at it, though. I've never had it be completely stuck, just slow to advance.