Your customer should not have to copy and paste the tracking id. Clicking the link should open a window to the tracking detail page. Over time, the tracking link may change. I do not use UPS so I do not keep up to date with there links.

You have to update the tracking link. Go to Admin->Configuration->Ty Package Tracker. By default, UPS is carrier 2. Change that tracking link to
Code:
http://wwwapps.ups.com/WebTracking/processRequest?HTMLVersion=5.0&Requester=NES&AgreeToTermsAndConditions=yes&loc=en_US&tracknum=
and it should work.