The Johrzeit is positively & absolutely only held on the date of the location where the person expired:- i.e. in your case [or example?] on Tammuz 3rd.
However, if the relative in question heard about this tragic loss and is not traveling to the interment, so would effectively commence laws of Shiva immediately, s/he would count the 7 & 30 days from his/her date of Tammuz 2nd or 4th respectively.
If this relative then requires to fly across the Jewish date line during the Shiva, s/he would still observe his/her 7 days, even though this would if going from Far East to Far West would then be on his/her 6th Hebrew calendar date, or if going from Far West to Far East would then be on his/her 8th Hebrew calendar date.