This is because the word "did" is a verb itself and is likely being used as a finite verb in the sentences you're thinking about.
So what's the deal with the present tense? Well non-finite verbs (also known as verbals) do not show tense and no longer function as verbs.
We wouldn't say:
I did cleaned.
And why not? Did is the past tense of do and we're talking about something in the past. Well it's because we don't need 2 actions in our small sentence, what we need is something to describe what exactly we did. In this case we use what's known as an infinitive. Specifically a bare infinitive (because it doesn't have the word "to" in front of it).
You can learn more about these by reading the articles linked within. Hope this helped you understand.