The acceleration of the universe was not discovered in Hubble's time, but in the 1990's by many observations of specific types of supernovas. You are correct in that Hubble's graph shows velocity, not acceleration, however your argument that the since older galaxies are moving away faster than closer ones means the universe is decelerating is not correct. Objects within expanding space naturally recede at different velocities depending on how far apart they are. The further apart two objects are, the faster they recede from each other. This holds even when the expansion is steady and is neither accelerating nor decelerating. Let's be clear here. In this context, acceleration/deceleration means an increase or decrease in the rate of expansion, not the velocity of objects.
There are many posts here on PF's cosmology forum explaining this, so I suggest you start there. I believe the link in Phind's signature block may also help.
Now, since this thread's topic is about a video that inaccurately explains expansion, I have deleted the link to your twitter and am locking the thread. If you have specific questions about expansion, you may start a new thread in the cosmology section.