Issued just for this occasion. It took 11 months to add that last star to the flag as noted on this token.
The obverse has the date of admission to the union, August 21, 1959. The reverse has the date July 4, 1960. Before July 4th date it has the words 50 STAR FLAG OFFICIAL.
Now I get it. Like you, I wonder why there seemed to be an eleven month delay to producing a flag with 50 stars.
I was curious so I looked it up - when Alaska was admitted, the 49 star flag was also official on July 4, but in 1959. Alaska officially became a state January 3, 1959, so that time it was six months before the new flag. https://www.americanflagstories.net/flags/49-star-flag-1959