Yes, you are right, the "transient" is a simplification and one actually needs to find the point, where the sample is supposed to be on the beat. I think eventually, one needs to employ critical listening to find that point. In any case, it's usually after the start of the audio signal.
Btw: "quarter of a second" is 250 ms, which is actually a lot. Some people here complain about things in the range of 10 ms, which is approx. the threshold where (at least some) musicians start to hear that something is out of sync.