Semicolons start a new thought, they don't mark an aside that lets you return to the original line of thought. Like in their example:

> For example: When you read this sentence (in your mind) it should feel complete and correct. Perhaps you read in your own voice — something I don’t normally do — or without one at all.

I would have used parentheses in both places, and semicolons don't work in either one:

> For example: When you read this sentence (in your mind) it should feel complete and correct. Perhaps you read in your own voice (something I don’t normally do) or without one at all.