The tutorial (I have the same course) is using an older version of Blender. As you can see in the screenshot in your comments, the Image Sequence node does not even have a field below the Color Space option where you can switch the Alpha.
To use the alpha channel of the PNG image, you can plug it into a Set Alpha node with the default Mode: Apply Mask. The Image output then produces an image with "correct" transparency.
By the way, if anyone is interested in the tutorial on compositing, Martin has uploaded that part as a free tutorial on Youtube where he is using Blender version 3.0.0 Alpha: Introduction to Compositing in Blender
As you can see there, his transparency looks the same as yours before he is using Alpha Over nodes with Convert Premultiplied enabled: