Each banner's apps may also restrict your choices and deals to that particular banner. For example, in places where Shaw's and Star Market coexist, deals added on the Shaw's app will also work at Star Market, even though the same deals may not be available on the Star Market app. (certain deals don't even show up if you have the flagship Star Market store selected, but the deals added while having a different store selected will work anyway!) The Star Market app will not show Shaw's stores and vice versa. I'd imagine if you're in California, Albertsons and Safeway/Vons might have a similar behavior.

Here's a map of the divisions. It is outdated though as ACME has spread into New York and Connecticut as well