This is not precisely a tax on millionaires, it's a tax on people that earn in excess of $1 million per year. While it is reasonable to assume that anyone making $1 million per year is a millionaire, not all millionaires make a minimum of $1 million per year.
So while it's perfectly reasonable for someone making in excess of $1 million per year to want to move out of California that presumes that their job which pays them such a high wage is easily transportable and that is not always the case.
In general, jobs pay in relationship to the general cost of living of the area that they are in. You can't assume that a job that pays $1 million in pretty much the highest cost of living area in the country will also pay that same $1 million in Detroit or some other rust belt city or rural area of the country.
If it did then *everyone* that lives on either coast would move to the center of the country. The reason they don't is because the high paying jobs aren't there and if they were there then the cost of living, particularly real estate, would be bid up so as to make that a high cost of living area as well.
So sure, anyone in CA that makes $1 million plus a year that can make that same amount in a low cost area of the country and who also doesn't happen to be tied to a $10 million home is perfectly free to move anywhere they want. However if that $1 million job pays only 1% less in another area of the country then they are better off staying where they are.