The matter was traveling at 99.99% the speed of light in the jet. While we generally consider space to be a friction-less vacuum for something like a spaceship, that isn't true for things like a stream of particles traveling across the universe. Even if the Earth stood still in this exact position for another 800,000 years (which it won't, since our galaxy is not stationary, nor is the solar system, and there is of course the expansion of space as well), very little of the physical matter from this jet would hit us.
Wouldn’t it give us way more than that? If it were traveling at 100% the speed of light it would take 8 billion years right?
The light has already taken 8 billion years to get here. The particles have also been traveling for that time and are only 800,000 years away now.