hello,
you are confused with two.
Vicm gives common mode when you signals applied. It is nothing to do with opamp architecture.

Vicmr_max means how max common mode you can apply to opamp and vicmr_min means how min common mode you can.

Always applied input common mode must fall in the range of vicmr_max-vicmr_min.

There is slight modification between the terms in your post and my reply, but you better follow this. Please have a look on Razavi book.

Thanks,
Raj.