How to un-segment faces / materials on a cylindrical shape?

Made these using the circle, push/pull, and offset tools. The large foreground cylinder has the material un-segmented, as it’s one of the only areas not push/pulled after the use of offset.

I didn’t notice until applying the material. Is there a way to fix it, or to avoid this happening again if I start over?

Without having your model to check it is a little hard to be specific but a few things spring to mind.
You may have applied the material to a group/component rather than the actual faces. Don’t apply the material without opening the group/component for editing.
If you have painted the actual faces you should be able to sample from one segment, and paint the others in turn, or turn off hidden edges and paint it all in one go, but be aware it won’t wrap aroung a full cylinder.