open_links_per_instance allows other transaction owned by the same user to go thru the link, that's why you can run more than one query.
open_links limits the number of connection TO REMOTE databases; you do no set this parameter on the target database.

I assume you have created on the target database a specific-private account to be used by DBlink to connect; am I correct?

If yes, you can set a limit to how many concurrent sessions can have that specific account.