There have been several posts showing affiliation information. You'll need to look back to find them.
With that said, the ARMER system is very complicated. Talkgroups will have assigned "home" sites/tower, be allowed to affiliated on other sites/towers or be denied to affiliate with anything other than that home site/tower. For example a Bloomington fire talkgroup may be assigned to Hennepin East as its home site, allowed to affiliate with Minneapolis City Center and denied affiliation with Minneapolis NS.
It's a methodology devised by system administrators.
Typically what I'll do when visiting Minneapolis, is program all the talkgroups I'm interested in receiving, then program all the sites in the Metro area in hopes that I can "catch" talkgroups of interest on at least one of the sites.
For your specific questions: Minneapolis Fire will be one Minneapolis NS. Owing to whether a Minneapolis fire unit roams into the Hennepin East area and gets a stronger signal there, they may occasionally be heard on Hennepin East.
"State" talkgroups such as DOT, State Patrol, etc., (and medical) in the Metro area will use Minneapolis City Center as their "home" site, but if they roam into other subsystem areas (Hennepin East or West, etc.) they will affiliate on those sites. (Confusing this even more, state patrol talkgroups are "forced" on all sites within their coverage area, so MSP metro west will be on City Center, Hennepin East, Hennepin West, Scott county, etc.)
St. Paul fire will use Ramsey and may be allowed to roam on Washington County, etc.