Try using the Edit menu to copy, then paste the Paint effect. Make sure your CTI (current time indicator) is at the first frame of the timeline when you copy and paste.
Another option, and the one that I would use, would be to duplicate the footage layer and paint on the top copy of the footage. When you have the animation the way you like it, you can create a new solid in the timeline, delete it, select the footage layer with the paint animation, then grab the solid you just created in the Project panel and hold down the Alt/Option key as you drag it to the timeline. This will replace the footage with the solid.
If you need to go back and do some more editing on the paint layer,, you can always grab the footage in the Project panel, hold down the Alt/Option key, andlace the solid with the footage.
If you have set in and out points for the footage so that it is shorter than the original, pre-compose the footage making sure to move all attributes to the new composition and trim the comp to the layer length. Now replace the pre-comp with the solid.
I would give that tutorial a D for explanation and a C- for workflow. It is a pretty amateurish approach to that kind of workflow. You don't have to do this kind of animation one frame at a time.