Hmmm. Unless there's a custom line going into the house it's not going to end up at 19V without a transformer. It'll depend on the installer if he taps the transformer off a 120 or a 240 line, and it may be selectable based on the wiring.

It's got less to do with science and safety and more to do with commodities. The manufacturer of the fiberoptic system (Fiberstars, maybe?) chose a bulb that was commercially available and designed a system that used that bulb. Halogen bulbs in a small form factor provide the quality of light needed.

For the OP's question why the 50W blew and the 20W didn't, I'd double check the specs on the bulbs. Putting a 12 V bulb into a (nominally) 24 V power supply is going to double the current through the bulb. It's possible that the 20W bulb is an extra-long life bulb with a beefy filament and the 50W is a wimpy bulb with a skinny filament. If you're really interested post more info about the bulbs.

Regardless, you're probably safe plugging in the new 200W bulb in and basking in the fiber-optic pool glow.