I have not much guidance to offer, just a few things:
1. take a deep breath. these things happen. don't panic don't stress too much.
2. if the exploit came because of a known issue that has been since patched, then updating your site software (joomla and extensions) will be sufficient after restoring from a backup.
the fact that this happens
AFTER 15 seconds suggests to me that it's probably some javascript inserted into every page:
All frontend (public) pages redirect to random websites after about 15 seconds.
So,
visit a page with javascript disable do it doesnt redirect, view source, and identify the snippet of code causing the redirect.
then try to search+find files on your server that contain this code.