Mind Crush VS Reinforcement of the Army (also Pot of Duality, Elemental HERO Stratos)

After those cards finish resolving, the gamestate is not open so first the turn player can activate a spell speed 2+ effect. If not, then you can use Mind Crush. In other words, you should be able to hit the added card with Mind Crush before they can play it, unless it is a card with a spell speed 2+ effect that could be activated at that time.

When a card's effect finishes resolving a window is opened where the turn player can activate spell speed 2/3 cards/effects as a response to that card's effect resolution, then that priority is passed to the non-turn player to respond with his own spell speed 2/3 cards/effects (time for Mind Crush) and then the Game State is open again for the turn player to play the card he added (which is now long gone by Mind Crush).