Scotto,Yes Tom, those are metric pipe threads equivalent to a US 3/8" per se. The poster asking is in Australia and they're metric down-under, so close enough to 3/8" with metric thread pitch.
As for using 3/16" on the larger barbs, just heat tubing up and add a drop of oil to it....slips right on and no need for clamps as well. You pretty much need a razor knife to remove it however.
Just to clarify...yes, it might measure about 3/8" in diameter but the actual pipe size is 1/8" pipe. Screw pipe sizes are notoriously wrong. I don't know where they started but take any NPT (National Pipe Thread) pipe/thread, inside diameter or outside diameter and you will not be able to measure the size...anywhere. Go to the hardware store and ask to see a 3/8" pipe nipple/fitting. It will actually measure close to 1/2" O.D. and well over 3/8" I.D. Some will say that 1/8" pipe is 1/8" I.D...Not so, just measure it. Same for 1/4, 3/8, 1/2 and on up. I stand by my earlier post in that the kit supplied tanks/petcocks have a metric machine thread,(about 3/8" in outside diameter) not a tapered pipe thread and therefore rely on a gasket to seal.That's why they put the little red gasket in the kits, to seal the petcock against the tank fitting. Tapered pipe threads seal by tightening the tapers together. Not trying to be argumentative, sir, just stating facts.
As for getting 3/16" tubing on the barbs...heck, if you can get it on, more the better. The smaller tubing would probably look cleaner than the fat stuff.
Tom