Even if this expired individual had prayed early Maariv for Leil Tammuz 4th on afternoon of Tammuz 3rd, or had lit Shabbos candles & recited Kidddush on afternoon of Tammuz 3td for Tammuz 4th {not that this is feasible, since Tammuz 4th can never be on a Shabbos} and then expired before sundown, his/her Johrzeit is on Tammuz 3rd.
If the person expired between sundown and emergence of 3 stars, approximately 38 minutes after sundown in the NYC area, this is way beyond the scope of this coffee Chat Room to determine if Johrzeit is on the outgoing or the incoming date. Check with the Rov of the deceased parent, so that entire family will end up holding the same Johrzeit.