Not exactly. The Giants announced their forthcoming move to SF fairly early in the 1957 season. The Dodgers waited until the season had ended and announced their move to LA in October of that year.
Also with respect to the Seattle Pilots, you got the year wrong. They played only one year in 1960 and then were bought out and moved to Milwaukee for the following year and renamed the Brewers.
I mistyped the year of the Seattle Pilots. It was 1969.