Depends on the seal:
Some aftermarket seals, the generic Teflon-coated type like I use, go in as shown in your picture. They come with an optional washer, too. If the bore where the seal fits in is perfect, you can go without the washer and it will reduce the stiction over small bumps by accelerating the fork a little before the seal stops moving: very effective. But, this arrangement can weep a bit of oil. Adding the washer below the seal will raise the seal up and often reduce the oil weeping, but the stiction increases because it locks the seal in place, not allowing it to wiggle and distort during acceleration. Adding the washer on top causes the same situation, but will not reduce the weeping if it is installed "upside down". This last option is definitely not the one to do.
The generic ones may also be run the other way, to reduce oil leaks, but will also increase stiction in the process. They function better as air fork seals this direction, which is the more commonly-installed direction.
If it is Honda's own seal, it's in upside down. Honda's seals are longer, and have a full metal shell, so no washer is required. Honda's seals have up to 3 lips in them, making them the worst at stiction over small bumps.
Your PO might have been experimenting with this whole 'stiction reduction' activity. It was a big deal during the 1980s and 1990s with these popular bikes.