punctually, punctiliously

Punctually or punctually describes the actions or behavior of someone or something that is prompt or on time--
He arrived punctually, and had to wait for the latecomers.
That bell rings punctually at noon every day; it's never a minute late.

Punctiliously or punctiliously describes the actions of someone who pays attention to the smallest detail or "punctilio" ( a fine point ), most commonly meaning a fine point of a code of behavior--
He observed all of the firm's regulations punctiliously, and never gave his employer an excuse to reprimand him.
If we all follow these rules punctiliously, we shouldn't have any more of these arguments.

Now that you know that, you can say--
"He followed the meeting's agenda punctiliously, and made sure that it ended punctually, at 5 p.m."

Note--"punctuality" is a noun ( thing or idea ), meaning promptness, or observance of the time set for meetings or engagements--
The school rewarded his perfect record of punctuality with a certificate of achievement.
"Punctual", meaning prompt or on time, is an adjective (describes a person or a thing)--
He was always punctual; he never kept her waiting.