No, I'm pretty sure they didn't update. Once I realized the issue I did watch them closer, to see if that was just a visual issue (have seen quite a lot of those in only a few days of playing - luckily they are usually gone after a reload).
I have had the behaviour you are talking about too, but that seems to be something different. I have units display outdated stats from time to time (hitpoints, remaining cooldown periods, number of attacks) but those stats usually update at some point (before they are actually needed). So it is only confusing, but not causing real issues. Also these issues only come up if there is a change to the units stats during a battle.
In my above case the unit enters the battle with full health after it was previously damaged in another battle. But it only has to figures in it, both in the units visuals and the stats and when I used them to attack they also did less damage and the stats did not update.
I actually haven't seen this issue again so far - only during that one session (meaning running the program without restart).