Agreement in Tenses?

Hi!

I read the following question in a TOEIC book:



“120. The travel agent said she would know the flight number and the precise arrival time ______ the airlines confirmed the reservation.



(A) during

(B) because

(C) when

(D) while



(Answer: C)” ((Longman Preparation Series for the TOEIC Test – Intermediate Course, by Lin Lougheed, p. 314))



I’ve understood the above sentence as:



“The travel agent said, “I will know the flight number and the precise arrival time when the airlines confirm the reservation.”



That is, considering the agreement in tenses, “will know” was changed into “would know” and “confirm” was changed into “confirmed”.



Am I right?

Thanks in advance.