My best guess is this.

FF14 works a bit differently from other MMOs in the Client/Server department. Using WoW as an example, the client sends your action to the server, and then the server confirms that it can happen, then the client responds. (It's why you'll start moonwalking, or just have a highlighted button but not do anything)

FF14 the client responds first, but requires confirmation from the Server for the result. Which is why when you're 90king, you can still push buttons, move around, and see the visual result of your input. (Until it catches up, or kicks you)

So, the guess is: You do all your mudras and hit the button, but the moment you input the third, while that's being sent to the server (and the 'confirm' coming back to change your Ninjutsu icon), you've already hit your Ninjutsu. Which is why you're seeing an effect 1 step early (confirmation didn't come yet) but getting the current step effect (ninjutsu command was sent with the 3 mudras attached)