A thin layer of oil does one thing: it lets the head glide instead of catching. That is the whole argument for it. Warm two or three drops between your palms, spread it over the area you are about to work, and give it a minute to settle.
Too much is worse than none. A slick surface takes away the grip you want, and the device skates. If the head is gliding over the skin rather than pressing into the muscle, wipe some back.
The oil that ships in the box with the device is the one we use. It is there because the order matters: oil first, then the head, then the work.