An important factor.
Climate
Climate
your local micro-climate is everything.
I live inside the "Lake Effect" band of Lake Michigan. My spring is often dominated by cool east winds, which will keep my daytime highs from March through May seriously chilled, some 10 to 20 degrees F cooler than a few miles west of me. So in early May, the official Chicago temperature at the airport ORD might be 75 or 80 F, I will have 50 to 60 F at my home. Japanese Black Pines need heat to wake up in spring. I often do not get candles developing until June and July, even though the trees have been out since May 1. For decandling to work, you candle prune 100 days or more before your average first frost. My first frost is around Oct 1 to Oct 15, this means I do not have sufficient time for my JBP to develop new candles if my JBP do not "wake up" until middle of June. So often in my climate JBP MUST be treated as a single flush pine, even though in theory they are a double flush pine.
Eastern white pine (Pinus strobus) and Japanese white pines are single flush pines in my experience. The Japanese white pine, is the "architype" of single flush pines. It is the techniques developed by the Japanese for JWP that set the standard for how to treat a single flush pine. It is fairly safe to assume that all members of the subgenus Strobus (the white pine subgroup of pines) are all singe flush pines. There may be a few exceptions, but it is a safe bet to treat all members of the white pine group as single flush pines. These may push adventitious buds and occasional needle buds over the growing season, but this does not make them "true" double flush pines.
Jack pine, Pinus banksiana is definitely a single flush pine in my experience. I have had a few adventitious buds pop over the summer, but never enough, and never reliable enough to consider a double flush pine. Jack pine is strictly a single flush pine.
I have no experience with Pinus rigida, I have a few young seedlings, too young to count as experience with their flushing pattern. However, everything I read suggests that pitch pine, P. rigida, will be a double flush pine in a long summer climate, zone 6b or 7 and warmer. Time will tell whether they will be "double flush" in my climate, zone 5b. Climate is critical in determining whether single or double flush pine techniques can be used.