The same applies for logging in. You can provide a login form in the Links part of the site, but the form needs to post the data to /forums/login.php (or wherever you have vB installed). It's easiest to cut and paste the login box from vBulletin into Links and modify the styles etc.
If I understand you correctly you are still having problems even though you are doing things as explained above. I am happy to have a quick look at your site if you want to PM me a URL.
One of my Links sites uses a modified version of this plugin to integrate very tightly with vBulletin, including areas like the newsletter subscription. For the most part it works pretty well and gives users a seamless transition between each part of the site .