My understanding is that while the above is correct as far as it goes, but remember that until a method of manufacturing it in quantity was invented in 1886, it was a rare metal, and the word would have been used very rarely and by only a few people in either country. (In 1884 when it was used for the apex of the Washington Monument, the metal was valued at about the same as silver)

By the time this happened aluminium seems to have been used fairly universally, including in America. In 1892, Charles Hall (independent inventor of the Hall-Heroult process used to this day) misspelled the word in an advertising flyer for his new method as aluminum, despite correctly spelling it aluminium in all his patent applications between 1886 and 1903. Webster's 1913 edition still used -ium, but apparently the advertising had been sufficiently effective (in that this was how ordinary people came in contact with the word) that the American Chemical Society declared -um to be correct in 1926, and US dictionaries and usual US practice have followed this since.

John