We must not forget that Reactions and Reserves are typings that cause the card to have a different color. And that is really the reason these types exist. Reactions in particular have a passive effect that occurs/can occur at an unusual timing, and this effect exists every time you draw the card. If these card had a normal color, it would be way too easy to forget those Reactions.
(and with Reserves, it's also future-proofing. I mean, they could introduce a card that lets you immediately move a Reserve to its mat upon gaining.)
Reactions have different rules about when/how they are played. No cards directly refer to "Reserve" or "Night" cards either, but they are also subject to their own rules about when/how they are played/used.
I don't think there are any rules for Reactions in general, are there? I mean, the Adventures rule book describes how Reserve cards work ("Reserve cards are tan, and have an ability that puts them on the Tavern mat") and the Nocturne rule book describes how Night cards work ("In your Night phase, you can play any number of Night cards"), but is there any Dominion rule book that describes rules for Reactions, as a type?
The rule book for the base set describes rules for Reactions:
Reaction: These are cards that can be used in some way at an unusual time. Any such use is spelled out on the Reaction card; for example Moat says it can be revealed when another player plays an Attack card. Reactions are used one at a time (which matters for expansion Reactions).
(p. 6).
All types have a description. And the last part holds true for triggers in general. But this is such a prevalent thing among non-Moat Reactions, it doesn't hurt to restate it here.
The Menagerie rule book has an entire section on Reactions:
Menagerie has five Reaction cards. Four of them can be played at an unusual time: Black Cat, Falconer, Sheepdog, and Village Green.
- Playing one of these Reactions using its ability (the text below the dividing line) puts it into play, like playing it normally, but does not use up an Action.
- If you play a card on someone else's turn, you discard it in that turn's Clean-up, unless it is a Duration card with things left to do.
- If playing one of these Reactions draws you another Reaction that can be used at the same time, you can use it, and so on. For example, you might have one Black Cat in hand when an opponent gains a Province, play it, draw another, play it, draw another, play it.
- When playing one of these Reactions, you can choose to use a Way if there is one.
- If multiple players want to do things at the same time - such as play Reactions - the player first in turn order (starting from the player whose turn it is) goes first. This may change who wants to do what; after each thing, start again from the first player and see who has things to do.
- Sometimes a condition occurs that allows a Reaction to be played, and that Reaction creates a second condition that allows Reactions to be played. Resolve all Reactions for the new condition and then go back to resolving ones for the first one. For example one player gains a Province, and another plays Black Cat. Gaining a Curse from Black Cat allows players to play Sheepdogs; after resolving those you would go back to see if players had more Black Cats to play.
(p. 4).
These are just rule clarifications that apply to "Reactions that can play themselves". The reason they went for this route is because they didn't want to state this four times, and it would also ease things up when a future expansion has more of these kinds of Reactions.