I use that exact low voltage alarm when I use my 2S. I don't have any puffing on my Lipo's (I have like 12 of them in different shapes and sizes).

What I do is set the alarm to sound at 3.7v and only run the battery down to 3.80-3.82v, meaning the alarm do not sound. I use a count-down timer on my radio.

By the time you take it out of the car the voltage will rise to around 3.83-3.85v which is my storage voltage.