The problem with your rule is that it is oversimplified and misleading. However, that is unfortunately a common way of teaching English in school. Teachers tend to oversimplify the grammar to make learning 'easy'.
The rule such as "the verb must be in the plain form when followed by 'did'" is not applicable in your case because the logic suggests that if X is followed by Y and Y is followed by Z, it entails that X is followed by Z. This is very misleading for the learners of English because it implies that all verbs that follow "did" in a sentence must be plain.
As a non-native speaker, the general rule of thumb that I think is accurate and has never led me astray is that:
A verb should be in the plain form after "did" only when there's no other verb intervening between them.
This is because the verb that follows "did" is usually the complement of and therefore is licensed by (dependent on) the verb "did". So in this case, only the verb "have" is in the plain form. "Figured" cannot be in the plain form because the verb "have" intervenes between "did" and "figured".