The difference in day length between a show-winning bloom and an open-centered bloom is not a lot. Most varieties, as the days shorten, will go from a fully-double bloom to an open-centered bloom in a period of only 2-4 weeks. At my latitude (and without cloudy days) this happens starting the third week in October and by early November almost all varieties have gone "open centered".
There are some varieties (at my latitude) that will only have fully-double blooms for about a month every season. I notice this especially with the Ball form of dahlias. Varieties like Clearview Peachy will have beautiful blooms for about a month, when the days are the longest (at bud development stage) but will be open-centered the remainder of the season.So, I guess this would be a combination of photoperiod and genetics?
To summarize, for me the most important cause of open centers is the photoperiod.