Hi,
No, with the override feature the results should be filtered on the results page as well. But in this case the issue is, that the page where the search is redirecting is not the results page (for example, this is the default results page), but to a different URL, which is not the results page itself – or at least it does not seem like it is, as the layout looks very different from the URL above.
You can place the same search widget to the results page, the filters will be remembered and passed on after redirection – but again, this only works on the search results page.
It wont work with other, different type of filters (from a 3rd party plugin, theme built-in etc..) as every filter uses a separate interface and query variables to pass the data to. Basically connecting all different kinds of filters is not possible in general.
Redirecting the results to a custom URL will not automatically place the results there, it is for cases when there is a custom results page permalink structure, and the plugin needs to be adjusted for it.