No, they don't. That was a problem with my first rack on my first bike. Two things happened: 1) I no longer shop at that LBS. 2) I'm very particular about my rack legs now.
No, the rack doesn't sway, but my three-year-old, el cheapo grocery panniers do. See how saggy, baggy they are in the photo? That can turn into sloppy, floppy on the road. The rack is a rock, though. Are you sure it's not your panniers swaying like mine do?
The Jandd Expedition solved all my rack problems on my first bike. It kept the panniers out of the spokes (see above) and it moved them back, away from my heels. I never experienced issues with that rack.
Jandd Expedition on my '06 Giant Cypress DX hybrid.
Why are you using the Tubus now if the Jandd was all that? I'm very fond of Jandd, but I'm not the sort of consumer who has experience with all models on the market. I use what I have until it busts, but I don't see my Jandd racks bustiing during my lifetime. I have broken a couple of Blackburns.