Okay shaz, I just did some battle testing and I've found that it doesn't make a difference whether you select battle, turn or movement. Even if you have a combination of the three they all initiate as soon as the condition is met.
So yes, it the character did fall below 50% on the first turn, assuming that they were at least 76% HP when the battle started, then both groups would appear simultaneously. But on that note, I found that if I entered let's say the boss battle with my characters HP already below 75%, then the first group of thugs would appear straight away at the start of the battle.
Maybe a way to try and avoid this would be (a) to make your character start the battle at full health. (b) make sure that the boss is unlikely to knock your health below 50% with one hit.
It could be more like an in game clue to the player that if their character looses over half their health in one hit from the boss their level obviously isn't high enough.
Hope this helps.