Puzzling negation in a beginner's grammar book
I understand everything they say. 他们说的我都懂。

I don't understand all they say. (I only understand some of what they say.)

他们说的我不都懂。or 他们说的我不是都懂。Here using 不 or 不是 makes no differences.

I don't understand anything they say.
他们说的我都不懂。

So 不都 means not all, ie maybe some, and 都不 means all not, ie none.