I can guess what was happening, based on a similar thing I used to do in Australia.
111 was either a number for something or possibly nothing (doesn't really matter what) - but it was a free call. So you dialed that, and the payphone decides to allow the call without you paying.
Next, you 'hook flash' the phone. This is basically where you hang up and then let go very quickly. Google that term for more info on it. This causes the exchange to either put your current call on hold and give you a new dialtone, or possibly just hangup the first call and give you a new dialtone. But the hook flash was so fast that the phone itself didn't register the hangup - so it still thinks you've on the initial call to the free number.
So now you've got a dialtone, and a phone that thinks your call is free. So you dial any other number. The phone itself thinks the call is free. The network thinks the payphone is charging you for the call.
Who's paying? Whoever runs the payphone. Presuming that was the phone provider themselves then it wasn't real money they were paying for your call - or at least not unless you were calling overseas...
For many years Australian pay phones had a similar thing, however after the hook flash the keypad was disabled so whilst you had a dialtone, you couldn't dial a number. The workaround was to use a small battery-powered tone generator and hold it to the microphone - it sent the dial tones (DTFM tones) down the line and your call went through.