私は洋子を説得してタバコを止めさせた。

English Translation

I persuaded Yoko to give up smoking.

The TTS is wrong and the transcript is correct. 止めさせた should be pronounced as やめさせた.
If you say タバコをとめさせた, that suggests that the cigarette itself was automatically moving, and Yoko blocked the movement as per my request. It doesn’t make sense.