Yeah I don't think you are meant to be able to (right now) do both Omni and custom queue. To my experience, it's whatever is queued first gets priority. I've been queued for Omni raid, then go in and queue a custom solo and neither will pop till the raid goes off. I mean really....shouldn't a solo pop immediately?
That always gets me - seeing the message that I can enter a solo when all players are ready, and then having to wait for a while. Screaming, "I'm ready, you dumb @$$&%£€!!!"
I have had this happen recently with only omnibus queued. What I noticed is that I need to select the mission in the journal and have it active for it to complete, versus it being an auxiliary thing that occurs from completing the content regardless if the mission is actively selected in the journal.