Cylinders from the first picture: you have the diffuse color, which goes from red to null driven by a gradient. Looks correct to me, just like in your Mix shader node.
In the 2nd image, the black circle on top of the cylinders also looks correct, since that part of the geometry isn’t affected by light (emission shader doesn’t receive light, unless you use it mixing or adding to a diffuse). The only doubt I have is if the gradient should appear here too.
A question: why diffuse pass has lens distortion filter?
Answering myself: there is no vertical (z) gradient in the 2nd image (directdiffuselight pass), so it’s correct.
But, the correct original question was: in the 4th image (emissive pass) shouldn’t it go from bright red to black?
Again the image is correct: the gradient starts from black (a thin layer of black at the very bottom) and immediately gets red as the gradient goes > 0, since the red emission strength is quite high. (i.e 0.010 in the gradient translates as 0.63 red emission)