Do not switch to same app on attached (external screen) my problem might be pretty straightforward, but yet, I can't get its roots.

I have MacPro laptop and attached external monitor to it. I'm not doing screen mirroring and I have 3 workspaces.
So when I switch workspaces on mac -- my external screen persists.

the question is: say I have google chrome opened on my laptop and another window on my external monitor. Than, say, I switch to other application on my external monitor (Sublime editor) -> I have Sublime on external + google chrome on laptop. Than I switch to other application on laptop. But When I switch back to GoogleChrome on laptop -> Sublime on external monitor is also switched to Google Chrome. I don't want this behavior. I want applications to be switched separately on laptop and external monitor, and not to be synced as it happens now. is it possible?
It sounds like you're breaking the Spaces paradigm by having one app over two Spaces. If you do that, behaviour will be at best unpredictable. 

You could possibly mitigate this by unchecking System Prefs > Mission Control > "When switching to an application, switch to a Space with open windows for the application" [but this is untested as I don't use "Displays have separate Spaces".]