Enable multiple sites serving on mailman web

We deployed mailman suite(exim4 + mailman core + mailman web) for our mail list server and now we have been asked to serve multiple domains in mailman, we found it's quite simple because we can create different domain on website. But we still have a problem that how to split these domain lists to different mailman web server Assuming we have two lists.

1. lists.a.com for mail and mailweb.a.com for mailman web
2. lists.b.com for mail and mailweb.b.com for mailman web

and we deployed two instances of mailman web containers, they use the same image and configure same mailman core and databse except that they have these two configuration differ:

1. SITE_ID =1 and SITE_ID=2
2. SERVE_FROM_DOMAIN=mailweb.a.com and SERVE_FROM_DOMAIN=mailweb.b.com

We thought it would lead to the lists seperation by domains when visiting different domains, but it seems we can see both of the domain lists no matter which we visit? How can we achieve this? Thanks

TommyLike