B made a technical error, in both her original deadline specification and in her follow-up message to you, to imply that “12pm” has a well-defined meaning. It does not. 12:00 noon is neither ante meridiem (before noon) nor post meridiem (after noon); it is exactly noon, and it should be referred to as such (http://www.npl.co.uk/reference/faqs/is-midnight-12-am-or-12-pm-faq-time).
Likewise, 12:00 midnight is exactly midway between one noon (i.e., meridiem) and the next, so one might argue that it has equal right to be called either am or pm. Midnight is also neither an “am” nor a “pm.” You can remove all ambiguity by referring to it as midnight.
You can usually infer from context whether a speaker means 12n or 12m when she says “12pm,” which is surely why most people continue to do it. But in the case of your deadline, I’m with you: I might also have assumed that a more likely time for a deadline would be midnight.
I think that both your note and B’s response were respectful and polite. You should be glad you asked. Asking saved you and B from missing your schedules. Had her response been different (she could easily have answered in the opposite way, because of the undefined-ness of “12pm”), it might have saved you from mistakenly prioritizing your application over something more urgent.
There are some fun stories on this noon/midnight topic at http://www.theguardian.com/notesandqueries/query/0,,-1752,00.html. Search for the string “3.07” for one that I found particularly intriguing.
:00.12:15is after noon, so it's PM. The zero minute of the hour follows the same rule as the rest of the hour. – Barmar Feb 27 '15 at 23:48