Don't know about "pumpers" but I stopped using any diesel prone lubes based on "dinosaur oil extracts" (petroleum based lubes) in my HW springers a couple years ago! I've been using only non-dieseling space station lubes called Dupont Krytox GPL205 for ALL lubing of my springers.
As far as "one drop through the transfer port goes", that's a throwback to the days of leather piston seals when the low powered (compared to modern springers) leather seals needed oil to function properly. Matter of fact, the famous Cardew experiments "proved" that the guns of that era got a major portion of their velocity from the dieseling oil in the seal. This "burnt off oil" needed to be replaced occasionally hence the advice to add a drop of oil every tin of pellets. As a side note........before using Krytox I shot my R9 with completely dry piston, receiver tube, and piston seal using only dry powdered graphite as a piston lube. Worked a treat and contrary to Cardew's experiments I only lost 10fps (.177 Crosman Premier from 910fps to 900fps) with my oring sealed piston cap. There was indeed about a 1% drop in velocity dry graphite vs molly paste but with my synthetic sealed R9 there was very little velocity gain when using "dinosaur based lubes mixed with molly"!
Since modern springers have synthetic piston seals and there is no need to keep them wet with oil. When I first bough a springer from Beeman decades ago the owners manual advised the "oil through the transfer port" lubing procedure. Beeman even sold some sort of concoction called "Compression Chamber Lube" for that purpose, however years later Beeman stopped selling the "Compression Chamber Lube" all together. The owners manual was changed to with a warning that "the warranty was void on guns damaged by excessive lubrication" (a rough paraphrase). Even when Beeman advised the use of "Compression Chamber Lube" the recommended procedure was a drop through the transfer port only when the piston seal honked with cocking. Not soon after these owner manual warnings Beeman stopped selling "Compression Chamber Lube" all together!
For my R9 and HW95 I completely degrease the internals and then relube everything sparingly with Krytox GPL205, then I don't mess with the internals at all unless there is some maintenance work to be done. I do have to admit however that I break down my springers once a year during the winter months for an inspection and then a relube!
If the shooter is unable (or unwilling) to break down his springer (voids the warranty) for a proper strip and relube, then "a drop of oil through the transfer port if the seal honks when cocking" is the only solution.
