Without seeing a screenshot of what you mean I can only take a guess.
E to extrude plus immediately pressing S to scale should work as long as your transform pivot point has not changed. So the first thing I can think of is to ensure your pivot point is set correctly.
By default it should be set to “Median Point” which is also how it’s set in this part of the tutorial. The image below will show what to look for.

I hope this helps and if it doesn’t please post a screenshot! If you’ve sorted out what had gone wonky please let us know so future students who might run into the same problem will see your solution. ^_^