I marked the same seams as him, but it produced different results. I know it's incredibly vague, but any kind of help is appreciated. Thanks!
Looking at your image, it looks like your seams aren't marked correctly. You should have an unbroken seem (red line in edit mode) running up the whole of the side of the mesh. This line should connect to a ring seam (a full red ring around the mesh) on each end, that separates the ends from the sides.
As lemon mentioned in the comments, you may also need to follow the instructions in How to make a square grid for UV maps to get even quads in the unwrap.
It may be worth looking at some basic uv unwrapping tutorials.
Try to install TUBE UV UNWRAP plugin. (Follow active quads unwrap method might also work)
Select all mesh and after that a vertex on an edge where seam should be then pres "U" and chose tube uv unwrap.
This plugin will work only on uniform tube shaped objects. Afterwards you can subdivide faces you want.