Rewrite profile not working for external website?

I am trying to do a rewrite profile where /xyz/ goes to https://my.3rd.party.hosted.website/somedir/

When I setup the rewrite profile for a hostname which is hosted by my local BIG IP (different virtual server) , it works.

When I put the server URI to my 3rd party host, it doesn't work and instead it sends the request to my virtual server's pool.

Is there something I am missing?

Rule type: BOTH

Client URI:

/test/

Server URI:

https://www.google.com/ (as an example, not actually what I am using)