Does Reaper shoot above and below him when using Death Blossom?

Reapers ultimate actually hits everything around him in an 8 meter radius (360 degrees).

Quoting from my link:

Death Blossom is a very deadly short range damage dealer that does 360 degrees of damage all around Reaper. Deathblossom is best used when there are a lot of clumped up enemies in a short radius, as it can wipe all of them out easily as long as they do not kill you first while executing Deathblossom.

For more info you can check this: Reaper strategy guide

People have also been talking in reddit

Quote from Reddit link:

Currently, Death Blossom's hitbox extends way above what it appears to hit. A reaper is able to ult on the ground and kill a pharah well above him. The hitbox needs to be changed to fit the animation or the animation needs to be adjusted to fit the hitboxes because it's extremely frustrating to play against.

It seems Reaper fires in all directions. His animation demonstrates that.

From this Ability Preview Video you can easily see flashes of red diagonally up and down. Demonstrating that he does fire up and down.

I was playing reaper last night when I panic ult'd; consequentially I have anecdotal evidence to proffer here. I was in the room to the left of that low spot at the very beginning of Watchpoint Gibraltar. I was located at ground level, the enemy Mei located almost at the top of the stair case leading up. Much to my surprise, my ult actually killed her.

So yes, it would appear as though reaper's ult has a considerable vertical hitbox at least above his character. Based on this along with Blizzard's 8-meter radius description, I would assume that it's an 8-meter radius sphere.