Problem is the wording is weird for that. That warp light line you get is from completing the primary objective on any floor including chest floors themselves while you only get the warps to the chest floor from bosses. On top of that the known triggers for chest floor are omen number related completely divorced from getting light on those kills. But the rest of the line says about when defeating monsters which pretty much rules out secondary objectives but also puts primary in not the best spot since you can get a free floor though that is rarer so might just be an oversight
As already said the larger and smaller have to do with path the rest of the warps all look the same and there are no choices well outside of Ou runs. Another odd thing this would be the first time the game would give us pre knowledge of a chest floor. Normally it's hit the warp and bam if it sends you somewhere else while giving you a weird message you win
Also to note that light messages both for primary and secondary are part of the acknowledgement for credit towards a card. So the full notes on this if all of it is taking literally and assuming no translation issues gives mixed messages. I fear something may have been lost in translation