Hama's dad and the mysteries of Q are now one and the same, because we learned that Hama's dad, despite disappearing 6 years ago, actually accepted a job 3 years ago. And his last job was for Q.
I think it's just that they "stank" when they were working for the first thing that hired them. Yume was able to evade that smoke thing covering the entire city; staying just out of their sight was probably pretty easy after a while.