No, the "Jock Tax" already exists. It exists in every state that has professional sports teams. For most professions, work that is performed on a long-term basis in another state is taxable in that state. For pro athletes, any work income that is generated in that state by both home and away athletes is taxed on a proportional basis.
As an example, 50% of the work income generated by Milwaukee Bucks athletes (41 home games of an 82 game season) is subject to Wisconsin income taxation. Because the Bucks play 4 games in California - one each at the Sacramento Kings, Los Angeles Lakers, Los Angeles Clippers and Golden State Warriors, 4.88% (4 games of 82) of Milwaukee Bucks' athlete salaries are subject to California income taxation. This income taxation process is repeated in each state a pro athlete derives income.
Walker's proposal is to divert these already existing NBA athlete income taxes from the Wisconsin state general fund to help pay for construction of a new downtown Milwaukee Bucks arena. The argument posed by tax supporters is that if a new arena is not built and the NBA compels the Bucks to move, the State of Wisconsin will not generate the Jock Tax for the state general fund in the future.
btw, it is not known if Walker's proposed Jock Tax diversion also applies to the near-term work income generated by the minor league hockey teams and or major league indoor soccer teams that might play in the new arena. Those Milwaukee sports franchises like their current venues and have no need or benefit in a new arena.
So this is not a new tax, but simply specifying where an existing tax will be used.
Will any general public revenue be used to build the new arena?