The reasons for the link are not fully understood, but it has been suggested that the amount of solar radiation we are exposed to in the womb is a key influence. The amount of radiation varies according to where you are in the world, what time of year it is and cyclic changes in the sun’s behaviour. The Equator generally gets the most radiation, and in the northern hemisphere, the usual radiation peaks will be in June and July, but there will be variations from year to year according to “solar cycles”. Every 11 years the Sun goes through a cycle when the magnetic field changes and the number of sunspots grows and dwindles. This affects the amounts of radiation produced.
The Maine researchers suggest that high radiation levels either stress the immune system of embryos and foetuses or cause small mutations in their DNA, which can either predispose or protect from disease, mould brain characteristics and influence length of life.
So the reason that people born in December might live longer could be that they were conceived in March, possibly avoiding the most harmful affects of radiation early on, when the embryo is at its most vulnerable, but also avoiding very low levels of UVR that might predispose people to certain conditions.
The assumed general mechanism in biology is good, whatever you might think of the rest of the theory; it's essentially covered by the reliability theory of aging - biochemical damage, caused by radiation or otherwise, lowers remaining life expectancy by reducing or destroying the functionality of component parts in the machine that is you.
The reliability-engineering approach to understanding aging is based on ideas, methods, and models borrowed from reliability theory. Developed in the late 1950s to describe the failure and aging of complex electrical and electronic equipment, reliability theory has been greatly improved over the last several decades. It allows researchers to predict how a system with a specified architecture and level of reliability of the constituent parts will fail over time. But the theory is so general in scope that it can be applied to understanding aging in living organisms as well. ...
In reliability theory, aging is defined through the increased risk of failure. More precisely, something ages if it is more likely to fall apart, or die, tomorrow than today. If the risk of failure does not increase as time passes, then there is no aging.
Some interesting studies are quoted in the article on solar radiation, but it looks very much like a case of having a hammer and seeing nails in everything. It is logical to suppose that demonstrated variations in human longevity and disease by location of birth date in solar and seasonal cycles have something to do with the sun at root - but that certainly doesn't mean that the sun is the direct cause of the biochemical damage that leads to such variations. It might be solar radiation, or it might be one or more differences in other systems caused by variations in solar radiation - diet, weather, hormonal changes, behaviors ... just to rattle off a few. There are certainly many more.
Once the article starts in on the distribution of mathematical or creative ability by latitude, with an eye on solar radiation as a root cause, I think it's completely lost in the sea of secondary, cultural and population-level genetic effects. There really is nothing of use to be said about that; more hammers in search of nails.
But back to aging: the interesting part of reliability theory as applied to aging is that is suggests we are born with a certain level of damage already present. The Strategies for Negligible Senescence outline a list of classes of biomolecular damage that can be demonstrated to contribute to age-related degeneration, much of which falls into the camp of accumulated biochemical products of metabolism - which one would not expect to see to any meaningful degree in the newborn. That doesn't leave too many types of damage that might be present in infants, either as a result of developmental errors or some process with the sun at it's ultimate root - missing or malfunctioning cells in important populations (such as stem cells, for example), and genetic mutations, essentially.
Once we can repair these forms of damage in adults - as a part of the effort to develop working rejuvenation technologies - reliability theory suggests that humans would gain some modest benefit in the longevity (or at least life expectancy) stakes by applying the very same rejuvenation techniques to the newborn as well. Science is interesting, is it not?