I dogsit a shi tzu (sp?). When she was younger she was prone to throwing up when she hadn't eaten. Similiar to Yorkies, this breed has sensitive tummies.
As someone mentioned above, empty tummy = yellow bile. This dog wouldn't eat the first day that I dogsat, but never threw up. Maybe her kibble that I gave her by hand as treats was enough to keep her tummy quiet.
Now, with my own 6 mo old yorkie, I keep a bit of kibble in his bowl all the time. LOL, kinda lost my train of thought with the noise that started up outside.
Oh yea, training to puke in a certain spot.... Dogs seem to have a difficult time focusing on anything but this automatic reaction that their body is having at the time to try to decipher what you're telling them.
Even if you say "Good Boy!" after they've thrown up in a desired location, I imagine that the dog is still absorbed into what just happened to them and what's now in front of them (the bile) and maybe even a little scared.
I would refrain from picking up a dog to remove it from, say, the bed while it's tummy is having spasms! Have always layed the nearest magazine in the target area hoping that stuff would land on it.
Of course, you can't do that if you're not around or awake.
Just my thoughts and trying to see it from a dog's point of view.