If it's implemented as: if you click on your responses tab in you profile, then all the new numbers on the tab go away, then I understand. It should be asked specifically for the case of "1 new response".
If I click on a notification on StackExchange, inbox. When I later navigate to my profile page (it doesn't do this on MSO, but does on some other sites), there is still a bubble with a number of responses on the responses tab, even if it's only one -- and it's relatively obvious I viewed it.
Does that clarify it?