Doesn't Esdeath say that Akame was using her trump card?
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Or maybe she was referring to Akame's own strategy as a trump card.
I heard the anime is not canon though.
Edit: Another question. Are Kurome's puppets controlled by her own reactions, their reactions while still alive or a combination of both?
You must have missed that part when the anime was confirmed canon (or, well, alternate canon) by the manga's author. Not to mention, Murasame's trump card even received a bit of hype from Lubbock - it certainly can't be that simple and what the anime showed actually fits the Teigu quite well.
Also, you know how it goes with translations. A "trump card" in reference to what some Teigu have, is "oku no te" in Japanese and it more literally means "secret skill", and has been translated as such on several occasions as well. Esdeath might have been talking about something more generic.
From what I gathered, it's both, but mostly it's Kurome's command. She can't control them completely apparently, at least when there are many of them or when she is weakened. For example: Henter was stabbed by Chelsea when she transformed into one of his fellow tribesmen because of his memories of them. Wall was defending Bols partly because it used to be his profession (he was "a famous guardsman"). Natala was protecting Kurome because he used to be her friend. So, some of those things can be used to Kurome's advantage, and I guess she simply lets that happen instead of assuming direct control.
Now, we don't really know whether she can 100% control them or not, but I think that she can, or could, when using less puppets and while she was healthier.