Its important to remember that different bins are not different models, but rather LEDs that are tested and sorted based on their efficiency. They are manufactured the same way, but inevitable differences in the manufacturing process cause some LEDs to be less efficient than others, like CPUs.
Warm tint bins are not available as "R2s" yet, since the manufacturing process can't currently mass produce warm tinted LEDs with the "R2 efficiency."
Marduke, flux and tint bins sort of are related, in that the current maximum bin for warm tinted LEDs is less than that of the bin for cool white LEDs.
I'm not sure that I know what you mean by saying that tint and efficiency are not exclusive. Currently, cool tinted LEDs have higher efficiencies than warmer tinted ones. If you want warm tint, you will have to sacrifice some efficiency, and to get higher efficiency you will have to sacrifice the warm tint. Therefore, you cannot have both maximum efficiency (currently R2), and a warm tint. In my book, this is what "mutually exclusive" means.
Is there some other distinction that I am missing?