Why my HS app is connected to accounts I didn't install it to?

I just developed and listed the App to Marketplace.

When I install it to the account that participates in organization, the App ended up to be connected to other accounts in this company. Is this correct behavior?
How can I then retrieve OAuth2 token for an account X if it is already retrieved for an account Y in previous installation?

@PKostetskiy , apologies, but I am confused. Could you restate the issue in a different way?

Ok, thank you for your reply!
It seems that I made wrong suggestions when I planned my app architecture.
Already understood my mistakes.