In my case it was a standard, relaxed interview. I'm also coming from Amazon, halfway through the training packet right now and things are going smoothly.
You should bring up your experience in package delivery. Not in the 'know it all' manner but to assure HR that you have a good idea what you're signing up for and are capable of doing the job. Be enthusiastic, tell them you're looking for a career and not just another job. I even talked a little s on Amazon during my interview, e.g., the unsafe driving, careless package handling, drivers storing envelopes on the dash, etc.
Expect the process to take some time (background check, DOT physical, and you might have to upgrade your license to a non-CDL commercial license) and try not to give notice until you've passed your road test and have a firm date for your in-class training. Try to save some $ in case UPS drags out your training. And don't just study the 5 seeing habits and 10 point commentary, the 5 rules re: backing, 8 keys to lifting and lowering, 5 keys to avoiding slips and falls, make sure to use these on your Amazon routes so you come prepared.
If you're doing well at Amazon, drive safely, work smart and respect the limits of your strength, you'll learn the ropes at UPS. Good luck!
