See, I don't know if I made a different choice or what during my first play through, but each opportunity I get to take a walk in Littanos, either Dynae accompanies me and that's it, or "I need to talk to the soldiers". Since you suggested it, I went and rapidly attempted each walk opportunity many times each so even if there is only a 10% chance, like I saw somebody say for Gifrix encounter, surely I would have gotten it. Either I'm very unlucky today or we are missing something...
P.S. Also, I interpreted wander around as take a walk as it is in Littanos. The next opportunity you get to wander around in the actual camp location, you are already at Yalen. Maybe that info might help.