Is the amplitude of a sine wave increasing or decreasing in this phase?
I think your issue is that you can't correlate the wave animation with the textbook chart one-to-one. The textbook graph shows the amplitude vs. time, so as you go along the x-axis towards the right from origin, the time increases, you are traveling "into the future". The animation is the opposite way of looking at the wave - the point of where the wave is generated (attached to the rod) is "the present", and the wave propagating away is in "the past". When the animation generates a sine wave (stating at zero), the amplitude will be increasing.