The Wichita Eagle reported that Brownback's critics Thursday treated the resulting tweet from the Republican governor's office as a strikeout.
Gordon signed a four-year deal Wednesday. Brownback's official account tweeted congratulations and said Gordon would save $1.8 million a year living in Kansas instead of California.
Brownback pushed successfully in 2012 and 2013 for massive income tax cuts to stimulate the economy. Kansas has struggled to balance its budget since.
Twitter users quickly questioned Brownback's claim.
A Royals spokesman said Gordon claims Nebraska as his official home and pays state income taxes wherever the team plays games.