Yes, that's undoubtedly the meaning that dinlot intended.
Между прочим, моим пиндостанским ушам, "to give (someone) a prompt" чем-то звучит "слишком по-британски", а "to give (someone) a cue" звучит более естественно -- but in either case, the basic meaning is подсказка. (From Googling, I found the near-synonym суфлирование, but it seems that this word is mostly used in the jargon of theater/film actors, and not in general speech.)
The only thing I would add to the discussion of -ся verbs is that they are ALWAYS "intransitive" -- meaning that in Russian, they can never be followed by an object in the accusative case (винительный падеж).