The tackle happened basically because Eileen is a musclehead and woefully inexperienced. She couldn't let Satsuki go to battle in her stead, especially since Satsuki had been teasing her with the whole 'go sip some tea' bullshit. So she did it impulsively.
I am really enjoying the fact that that Cyrille and Mii are inevitably stuck with all the killing (Cyrille's mace is always sporting blood).