I'm unable to reproduce this. The badges are certainly available to folks who use the mobile interface, and this is most likely a caching issue.
I just tested this with a different site and saw the "last seen" timestamp update immediately on my phone and when viewed in the browser on my desktop, but not when viewed in an incognito profile I opened up first.
This appears to have been fixed at some point since being posted.
I just put [stargate*] into the search box, and after submitting it the search terms were expanded to:
[stargate] or [stargate-sg1] or [stargate-atlantis] or [stargate-universe] or [stargate-movie]
Likewise, [star-trek*] becomes:
[star-trek] or [star-trek-tng] or [star-trek-voyager] or [...