Hybrid Model - Why differential of voltage equals AC component voltage?
But it is not the derivative with respect to time that is important in this case.

The hybrid pi model is the result of doing something called linearization (which you ought to be able to search on).  The notion is that you take the derivative around some input (in the video it appears to be \$I_1\$), build a linear model based on those derivatives, and then declare that the circuit behaves as the Taylor series approximation out to the first term.

The whole business of calling the variation an "AC" term riding on a "DC" term is an attempt to make it easier to understand.  If it's making it harder to understand, then just go back and look at that Taylor's expansion, and think about it for a while.