That's a frikking big coin you are resting the razor on!

Maybe you are being too gentle when wiping off the blade with tissue. As long as you avoid the cutting edge it's OK to wipe with a cloth/towel.

I find the easiest way to make sure a razor ends up clean and dry is to run some fresh hot water into the sink, rest the razor in the water (on top of a cloth for protection if you like) then let it soak for a minute or so while you tidy up other stuff. Take the razor out of the water and dry it quickly while it is hot. Tap the scales against the towel gently to remove drops of water from inside. Any remaining moisture will soon be gone because of the heat. I don't know if this method would be safe on exotic or wooden scales though.

Someone said olive oil can be slightly damaging to steel. I doubt it is responsible for what you are seeing. But if you can get some mineral, camellia (tea seed), or Ballistol oil instead they might be an improvement.

I'm going to throw in my usual warning about not using the blue Dovo presentation case. I have no proof they cause rust, but packing foam+moisture=trouble in my book.