The pashtus is that kavsah ain zakuk lah is because a partial kiyum is enough. Really, your candle should burn longer, but even if it burned 5 minutes instead of 30, Chazal said it’s enough.
However, if you use the lomdus of the Nimukei Yosef that I suggested last post, i.e. it is as if the entire process of burning takes place the second you start the fire, then kavsah ain zakuk lah is not because a partial kiyum is enough, but rather because it is as if everything is done already – you already have a full kiyum the second you light the candle.
There is a machlokes between the Terumas haDeshen and the Taz (673:s”k 9) if your chanukah candles go out before shekiya on erev Shabbos whether or not you have to relight them. On a regular night of Chanukah, when you light after dark, the kiyum mitzvah happens as soon as you light. Therefore, kavsa ain zakuk lah. On erev Shabbos, however, the kiyum mitzvah does not happen until after dark, long after you light the candles. Therefore, the Taz holds that if you still have time to relight before shekiya, you have to do so – as long as you can make an effort to get in the kiyum, you should. The Terumas haDeshen disagrees. Since Chazal said to do hadlakah before shekiya, once you light the mitzvah is done and kavsah ain zakuk lah.
If kavsah ain zakuk lah means a partial kiyum mitzvah is enough, then it would seem that the Taz is right. You need to do your best to at least have some kiyum mitzvah get off the ground. However, if kavsah ain zakuk lah means time or the future action that will unfold (or whatever other formulation you use) is compressed into the initial moment of lighting, then the Trh”D seems correct -- once the hadlakah happens, the kiyum mitzvah that will unfold later counts as if it occurred at that moment already.