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In the same article, there are 2 different "did ... do" styles.
I told my parents I didn’t want to come home for fall break,
...
I helped my dad pick out a few dates that coincided with Nate’s second fall tournament.
The first is "did ... did", and the second is "did ... do." Why?
Why? Because that is the tense of the clause.
I told my parents I didn’t want to come home.
You told them in the past, and your thought of not wanting to come home also occurred in the past.
You could easily say:
I told my parents that I am not coming home.
This is talking about your telling them in the past about a future action. Although the information conveyed is essentially the same, the difference is you are here referring to the action whereas in your original example you are referring to the point at which you decided on this action.
