They will all look the same in the viewport (multiple colors) regardless of the frame number, because their dynamics have been turned off. Static field of particles.

But if I render a different frame with MR, they will all be colored the same - directly related to the lambert assigned to them, and the image sequence they are based on. In that example, they are all a yellow color, because that particular image in the sequence is the yellow one. If I scrub one more frame and do another MR render, the color will change because the image sequence will cycle to the next in line.

I want the MR render to look like the first attached image.