Simple Past vs. Past Perfect

Hi!

I read the following question in a TOEIC book:



“103. The computer programmer realized he had forgotten to turn off the office lights ______ he had left the premises.



(A) after

(B) because

(C) since

(D) and



(Answer: A)” ((Longman Preparation Series for the TOEIC Test – Intermediate Course, p. 313))



I’ve understood the above sentence as:



“After the computer programmer had left the premises, he realized he had forgotten to turn off the office lights.”



I think the sequence of the events is:



The first event – forgetting to turn off the lights

The second event – leaving the premises

The third event – realizing that he didn’t turn off the lights



Am I right?

Thanks in advance.