I think I can see how your mind is working - you’re confusing the “alternating” part that’s applied to voltage and current with power.
By your thinking, the power is alternating too - but it isn’t. If it was, your electric oven would never get hot because the power/energy/heat would flow into the oven and heat it on one half-cycle, then immediately flow out and cool it on the opposite half-cycle.
Look again at that page. In the very first graph, voltage and current are both alternately positive and negative, but power (yellow) is always positive. OK, it has big ripples on it, but it’s always positive. And if you think about it, that must be true: P = V × I, and P is positive when V & I are the same, whether they are both positive or both negative.
Now if you invert one of those, say the current (because we usually use the voltage as our reference), you get diagram 4. Using exactly the same maths, power is always negative.
The only piece missing now is to relate the direction of current flow to positive and negative. Let’s say: if the current is flowing into my house when the voltage is positive and out of my house when the voltage is negative, then power is flowing into my house. If the current is flowing out of my house when the voltage is positive and into of my house when the voltage is negative, then power is flowing out of my house.