Quick filter deletes the unselected values from the underlying table.  You no longer have visibility to them, so you won't get the "other" data you want.

Look at SET ACTIONS (starting in V 2018.2 or 2018.3, not sure which one...)  This lets your user select multiple values, and then you build calcs using the set's IN/OUT capability.  All the "out" values would be your "other" value.

There are a bunch of Tableau KB articles and how-to videos on Set Actions, so I recommend you check them out.  I haven't done a lot with them yet, so I'm not the guy to guide you on best practices for them.

Okay, so this is a lot of work to get to your final solution, but I think I've figured out a way to do this. It's all pretty much just Tableau trickery.

First of all, we need union the data to itself, which will duplicate the data. Next, we'll use the new Table Name field to create an artificial Market name:

Market New

// Adjusted market name.

IF [Table Name]="Sheet1" THEN

    [Market]

ELSE

    [Region] + " Other"

END

Then we'll create calculated fields to get some additional details, ultimately getting to Amount New which will give us either the amount for the market or for "Other".

Total Amount

// Get the total overall amount for the region.

// Dividing by 2 to account for data duplication from the union.

{FIXED [Region]: SUM([Amount]/2)}

Other Amount

// Get the amount for "Other"

MAX([Total Amount])-SUM([Amount])

Amount New

// Amount depending on if it is a regular region or "Other"

IF RIGHT(ATTR([Market New]),5)="Other" THEN

    [Other Amount]

ELSE

    SUM([Amount])

END

Then we can build a view based on Market New and Amount New.

The trick here is that our filter is on Market and the union is handling the creation of the "Other" segment. You'll also want a filter on Amount New to include anything >0. Without this, the "Other" segment will always show even if all markets in that region are selected.

Take a look at it in action:

See attached.

Any time. Glad it worked!!