Everyone get confused by the difference between Gregorian and Julian dates.
Nicholas was born on May 6 (Julian) which adding 12 days in the 19th century becomes May 18 (Gregorian).
After the turn of the 20th century, the Julian calendar fell another day behind and so Nicholas was still born on May 6 (Julian) but on the Gregorian calendar it was now May 19.
According to a Russian Orthodox poster, the Julian calendar did not fall another day behind the Gregorian at the turn of the 21st century, so it is still 13 days behind even now.
However, Nicholas's birthday was Job's Day or May 6, but is now celebrated on May 19th.
So where ever Nicholas was on May 21, 1908 would have nothing to do with his birthday even with the change in calendars. In Russia, May 21st would be May 8th and in the west it would be May 21st. Neither of those days is his birthday.