Power of a controlled voltage source
It is quite possible for an ideal voltage source or an ideal current source to consume power in a circuit.
It's very important that you understand what these ideal sources do. You should think of them as constraining a voltage or current to have a certain value. If you think of them as creating voltage or current, or limiting voltage or current, then you will get confused in situations like this.
For a simple example, suppose we are charging a battery from a bench power supply. If we drew a rough schematic, both of these would be modeled as ideal voltage sources, even though the battery is consuming power. The battery constrains the voltage at its terminals to be some value because of the particular chemical reactions going on inside of it.