7 June is the technically correct date to observe the anniversary of Alexandra's birth on the Western calendar.
However, Alexandra herself apparently didn't care much for the way the new style dates shifted after 1900 -- a notation at the top of her diary page for 24 May/6 June 1918 says "my real B.D." A footnote at the bottom of the page explains: The empress's bithday had been celebrated officially on 25 May (old style), despite the fact that at the turn of the century the difference between the old and new calendars changed from twelve to thirteen days. From Alexandra's point of view, her "real" birthday should have been celebrated on 6 June (new style).