With SWR, often the answer is "there is no such single word."
Traditionally someone officially gives that as an answer, so:
There is no single word for "adding liquid to...". You just have to say "adding liquid to..."
Moving one step up conceptually and using 'making" is the best you can do here. If you're literally writing an explanation of how to make these drinks (a recipe, receipt, as it were) you would have to use "add water to" for that step - as you can see in recipe books.
In arcane situations (like, a science lab when adding small amounts of liquid in to some powder) you can use "wetting".
Please note that when the answer to a SWR is *"is no single word** for..."* then, logically, it's impossible to "give a reference" for that, since you can't prove a negative. (Except in the bizarre case that there's a research paper on the existence of such a term.)