Before we go to self oscillation as an explanation, let's look at how you have connected the chip, in particular the tab. The tab is connected to pin 2. In fact, pin 2 and the tab are likely the same metal piece, which is used as a holder for the die, as shown in the attached image. Pin 2 on your particular device is the output, meaning that if you connected the tab to ground for heat dissipation, you are shorting the output to ground. What would happen then is that device would heat up rapidly, and likely shut off due to thermal overload protection.
Another thing, NCP1117ST12T3G is a 12 V regulator, not a 3.3 V regulator. Maybe you used that as a generic name for the whole range of those regulators, but if you used an actual NCP1117ST12T3G, you've probably fried every 3.3 V chip on the output side, and maybe some of the capacitors as well if 12 V is out of range for them, and possibly created a short somewhere inside a chip in the process. The good news is that the regulator likely survived, so if you need a 12 V regulator in the future, you can probably salvage that one.