How do you know what spider needs adjusting when one of them is out of round?
You don't, so you just start with one crank and get the chain tension as even as you can, and then move on to the second one for additional fine tuning.
How do you synch up the cranks? Just slip the chain up or down teeth?
That's pretty much what you do, i.e., loosen the eccentric so that you can rotate it to create enough chain slack to remove the sync chain and then slip the chain one set of links at a time, rotate the eccentric (but don't tighten it just yet) to check your alignment until you get the desired crank phasing. Once you get comfortable working on the tandem you can leave just enough slack in the sync chain so that you can derail it by hand without loosening the eccentric. See video below. Warning: If you don't have enough slack in the sync chain (about 3/4"), you'll run the risk of getting your hand too close to the timing ring's teeth, and bad things happen when fingers get caught between a tight chain and sprockets.