I was going through "Video Tutorial 4: Parenting" when my cylinders were severely distorted when I parented them to the box, after some trial and error I found that this happened because the cylinders were rotated, they flattened and became oval-shaped. Is there a way to stop this from happening?
This is probably because your box has a non-uniform scale (meaning: a scale where the x, y & z values aren't all the same).
Your cylinder is being stretched along these axes in the proportions described by the box's scale. In general, non-uniform scaling with parent-child relationships tend to give undesirable results.