The jurisdiction requirement of 3 months is related to Filing only and not interview or oath. You need to file from the place where you claim residency (3 months requirement) which in general is the place where you file your income taxes from. There are certain exceptions in 8 CFR 316.5, the relevant one for military is 8 CFR 316.5(b). If OP filed from NY and then moved to VA and changed address, they do not need to wait 3 months in VA. I believe the officer is wrong here.
(b) Residences in specific cases—(1) Military personnel.For applicants who are serving in the Armed Forces of the United States but who do not qualify for naturalization under part 328 of this chapter, the applicant's residence shall be:
(i) The State or Service District where the applicant is physically present for at least three months, immediately preceding the filing of an application for naturalization, or immediately preceding the examination on the application if the application was filed early pursuant to section 334(a) of the Act and the three month period falls within the required period of residence under section 316(a) or 319(a) of the Act;
(ii) The location of the residence of the applicant's spouse and/or minor child(ren); or
(iii) The applicant's home of record as declared to the Armed Forces at the time of enlistment and as currently reflected in the applicant's military personnel file.
(b) Residences in specific cases—(1) Military personnel.For applicants who are serving in the Armed Forces of the United States but who do not qualify for naturalization under part 328 of this chapter, the applicant's residence shall be:
(i) The State or Service District where the applicant is physically present for at least three months, immediately preceding the filing of an application for naturalization, or immediately preceding the examination on the application if the application was filed early pursuant to section 334(a) of the Act and the three month period falls within the required period of residence under section 316(a) or 319(a) of the Act;
(ii) The location of the residence of the applicant's spouse and/or minor child(ren); or
(iii) The applicant's home of record as declared to the Armed Forces at the time of enlistment and as currently reflected in the applicant's military personnel file.