Orientation is especially relevant for ribbon tweeters such as those used by ADAM, as they do not have the same spread in both directions. Given that they're quite directional anyhow, orienting them incorrectly might well narrow the sweet spot. Other monitors, such as Genelecs, have ovoid-shaped waveguides designed to spread the signal on the horizontal plane, so the same principle applies to them, too.
Silk-dome tweeters are more omni-directional, so I wouldn't expect orientation to be a big deal for NS-10s. However, I do know that there were two variants of the NS-10 made, one meant to be horizontal and the other vertical. What they did differently for the horizontal model, I do not know. The tweeters
look the same.