This is the bizarre sort of thing that I can't help but look into. Now, this might fly as speculative, but obviously there isn't a great deal of published research to fall back on. Pimm's hasn't said anything about it and those dates seem to have nothing in common.

However, their website does contain one substantial clue: If you scroll down on "anyoneforpimms.com" far enough, you come across a side-scrolling table labeled "Factish." This seems to randomly spit out about a half-dozen Pimms factoids.

It's the fourth or fifth that seems to contain the hint: "From the shores of Sri Lanka to the officer's mess in Khartoum, by 1914 PIMM’s was already a pillar of the Empire."

Based on examination of the bottles, and the lack of any other indicator, it seems like Pimms is attempting to track the spread of the no. 1 liquor overseas. Presumably, they have some reason to believe the first bottle of Pimms in Peking entered in 1889, Paris in 1897, etc.

The fact that most of these cities were either in Europe or the British naval sphere at the time seems to support this idea.

Apologies for lacking anything more concrete--again, this is primarily speculative; mods, feel free to purge this. That said, I'm fairly confident in this answer and I doubt there will be much concrete documentation to ever answer this particular question.