This meaning refers to completing something correctly and in accordance with rules, procedures, or obligations.
The document was duly signed by both parties.
All complaints were duly recorded.
This meaning indicates that something happened at the proper time or as events led one to expect.
The package duly arrived the next morning.
She duly returned after completing the assignment.
This use emphasizes that a result occurred as a fitting, logical, or predictable consequence.
He ignored the warning and was duly punished.
The team performed well and was duly rewarded.