Yep, we called right after we picked up our bags and they told us to go right outside baggage claim to be picked up- you don't have to drag your bags upstairs to the shuttle area. They were there in under 10 minutes (I'm guessing closer to 5 minutes- it didn't feel like a long wait at all), and the whole thing went really smoothly. We prepaid the tip online when we paid for the reservation, and I seem to recall we tipped 15%.
I was bummed the price went up too- we are also going in June, and I liked the $61 price back in September better. But it's still worth it at $72.
Thanks for the info. Sounds like they are pretty efficient.