I suppose it could be used to include, as well as exclude. Really, I think I mostly see it used in introducing or requesting information, often lists. In that case, it's used to say "excluding this obvious answer", or "this answer that has just been mentioned".
Other than Washington D.C., list parts of the USA that are not themselves states, or part of states.
The answers are things like Guam, Puerto Rico, etc.
Other than oranges, name three citrus fruits.
Lime, lemon, grapefruit.
Your example sentence, well, it doesn't read naturally. Even fixing the grammatical number to more normal usage, we get
Dates are good (to eat?/for you?), so other than evening, they should be eaten in the morning.
That isn't a way a native speaker would say it, but if I hear or read that, I would assume that it meant
Dates are good for you, so as well as the evening, they should be eaten in the morning.
It's still not natural, but much more nearly so.
Basically, other than generally means "yes, we acknowledge that this item fits what we're saying or asking, but we want to put it to one side and focus on other things". So it both includes and excludes, depending on how you look at it.