This really sums up the problem with "phillips type" screws... There's SO many ways, SO many variants, So many permutations, then there's discount hardware that just has a universal "cross slot" drive, and so many screwdrivers with so many permutations of how they try to make those both universal and cheap, to get as many screws as they can with the same one. It's just a free for all.
My advice is that one needs options in "phillips" screwdrivers to select a best fit. It's gone so far as to say that it's not a standard, but a free for all.
Cool trivia about JIS screws. They're all but dead. That standard stopped getting maintained maybe (10?15?) years ago, and , and the Japanese Standards people allowed it to shift over to a DIN standard that was (essentially) a duplicate of it. Nearly (very nearly) identical, and all proper drivers are 100 percent backward compatible, no compromises.
I do suspect the dot may have a different meaning. It's very common for me to see one vehicle or machine that's ONLY got certain sizes of screws dotted, when they are ALL JIC/DIN standard screws. I haven't decided if it's diameter or thread pitch, because the ones in the Japanese truck cab, which comprises a large portion of my regular job, both criteria could be valid. It's the SAME two sizes of screws, the thread pitch on those two is ALWAYS fine thread, and I havn't found coarse ones to compare in that particular application.
From that I believe that the dot DOES indicate JIS (even if it's new enough to be DIN), but the lack of a dot does NOT indicate that it's not JIS.
Just observations, I've never bought the specs.