You have to enter the actual mission for the mountain pass. You should be able to get it from the civilian at the mountain pass transporter. Finish that mission and at the end is the shuttle craft that you see the recording from.
Yeah, it should be the one to infiltrate the hidden Tal Shiar base in the cave. You have to free some Romulan prisoners and then fight a handful of Hirogen with the base leader at the end. But once you finish the mission, don't exit. Go to the shuttle in the back and watch the recording. Make sure you submit the recording after watching it too, otherwise you have to redo the whole mission over again.
I had the same mission and I got "Kicked" and or Disconected prior to "Submitting the recording"... now I have a mission I can not go back into, and can not drop...
Wait 20 hours and you can redo the mission.
The Cave mission unlocked at Tier 3 has the cutscene mission at the end of the mission as well. The Cutscene mission for Tier 5 is at the end of the Ruin mission unlocked at Tier 4. There is no need to do the Ruin mission until Tier 5. I suggest buying EV suits for your bridge officers off the exchange before doing the Ruin mission. Otherwise, you have to purchase the basic EV suits for 100 dilithium each.