MacOS – spotify doesn’t care about mission control settings

Windowflow - free for a limited time and gives some options for different spaces and such.

Witch - 12,99 € and has an option that will only show apps in the current space.

WindowSwitcher - 3,59 € and it comes very close to your needs, check it out.

As far as an native solution to your problem: I don't think there is a setting or command that makes the application switcher behave like this.

Definitely check out WindowSwitcher I honestly think it is what you are looking for!

p.s. prices were correct at the time of posting.

It seems that what you are doing does not work the first time, but after 2 tries, it does. So do this to the 'When switching to an application, switch to a space with open windows for the application':

1. Turn it OFF in System Preferences → Mission Control
2. Turn it ON
3. Turn it OFF again.

You could also try typing this in Terminal:

defaults write com.apple.dock workspaces-auto-swoosh -boolean NO

...but that is said to only work in OSX Leopard on the website above but 'jgl777' over here said that it worked on his 10.8.3 Mountain Lion, so it's possible it could work on Mavericks. I would advise backing up if you do this, but you should be doing that even if you don't want to use this method!

Another option is to Ctrl + Click the application's icon in the dock and then click open in new window, this will open it in the current Desktop and a new window of the app.