Cooler water will cause the pressure inside to drop, but the housing electronics attempt to compensate for that - the only thing I can think of is that this compensation may not be exact and it's enough to trigger the alarm as you are too close to the trigger point. Does it come on straight away or after you reach a certain depth?
How many pumps do you make after the green light? I generally make three pumps after the light first goes green and find the light stays green in the water. As I noted above I do not think the extra vacuum will be an issue, one because it it is not that much lower and two is that air leaks faster than water. If the light stays green for an hour or two the housing is tight and not going to leak. The only time the extra pumps might be a concern is if you jump into the water 5 minutes after pumping it down.