I've used racks like that for 35 years. I use bungie cords to attach all kinds of things. Tying things up can be slower than with other methods, but it works. Be patient and thorough. Make sure the bungies are tight and have no risk of dangling or getting caught in the wheels or anything. When I tie up clothing or a backpack, I take care to tuck in any dangling straps, sleeves, etc.

You could use rope if you prefer. Or you could use those nifty ratcheting straps that have become popular. Be sure you're good at any of these skills before you take off. Bounce and wiggle the bike to be sure.