The theme you’re talking about isn’t a child theme. If you read the description, you’ll see it’s “based on the awesome TwentyThirteen.” This just means it’s inspired by and probably borrows code from TwentyThirteen, but it’s not a child theme.
As for a real parent-child theme relationship, the goal is that when the parent updates you just reap the benefit of the update. However, if the parent theme changes its styling or the IDs it uses for various elements, you might need to update the related code in your child theme to match.
Most parent themes will retain their IDs (i.e. #article), but there’s no guarantee.