How to use the past perfect tense with 'until'

Which one is correct? (Or both of them are?)

I did not understand until you had explained.

I had not understood until you explained.

Also,

We did not disturb him until he had finished his job.
We had not disturbed him until he finished his job.

Answer

Well, to be perfectly honest, they're all grammatical in that there are no syntactic or semantic issues involved.

With that said, when you're using until it's usually the preceding clause that uses the perfect construction, particularly because until is being used synonymously with before. So to me, I prefer the second sentence in each example.

For example:

I didn't understand until before you explained.

I hadn't understood until you explained.

We didn't disturb him until before he finished his job.

We hadn't disturbed him until he finished his job.

The past perfect typically indicates that the action occurred before another action, so it's used for whichever action occurred first, With these, it would depend on your perspective; but from a first person perspective, the second is correct.