Yeah, it's better to just get another Ripjaws X 1333 kit, since the 1600 kit would be restricted to 1333 anyway. No way around that, by the way. All modules will be forced to run at the same speed, timings, and voltage, so it just doesn't make any sense to add faster modules to existing slower modules.
Will the 1600 run at the same speed, timing, and voltage as the 1333 automatically or would I have to adjust some of those settings manually?
Well, both kits will be forced to run the same settings, regardless because that's just the way it is with only one setting for all modules installed. There's no way to run the kits at separate speeds, timings and voltages even if you could or wanted to.
With that said, yes, it should be automatic, BUT...
I'm not exactly sure if both kits will be happy with each other, though. You might be forced to reset the BIOS and then reinstall both kits for both kits to play nice (even then, it's not a guarantee that they'll work flawlessly together).
Iy's always a risk to run two different sets of ram that are not even the same speed, you just don't know how the motherboards bios is going to react. You could put them in and both work, but at the lower settings 1333mhz or they may not work right away and you may need to make a bios adjustment.
If it's at all possible you should pick up a set of the same ram meaning all 32 gb of the 1600mhz.
Is there a reason for going from 16gb to 32gb?