Commenting on the miners’ recognition of Divine intervention – the WSJ reported that the shaft through which supplies and food were delivered over the past weeks was 5″ (five inches) in diameter. As one of the posters above noted, the miners requested many things. The WSJ reported that early-on, one of the miners requested 33 Bibles, so that he could lead religious services in the rescue chamber.
So, I would suggest that both before, during, and after the rescue, these men recognized the One from whom the rescue came.