Power what? Besides your Internet modem, what requires power? Does the Cox-replaced 3-port splitter plug into an electrical outlet? If so, it's not just a splitter but a signal amplifier. The tech had to boost your signal to within operating specs.
Just as a reference point, all coax doesn't terminate in the outside box...your signal from Cox originates at the outside box. The outside box is a Network Interface Device (NID) and is the demarcation point between you and Cox.
Where are these other unconnected coax cables...in the outside box? If so, that's where you'd split your signal for the other rooms.
Where were the 2 televisions located...in the other rooms? Are those coax cables (for the 2 televisions) still connected to the Cox-replaced 3-port splitter? If so, those rooms are already connected for your MoCA adapters.