It assumes that the people with bigger wallets also use a larger portion (absolute money, not percentages) on the “thing” to begin with. If the billionaire and the middle class man uses 10€ on the same thing a month, and both stop doing it, then they both got the same amount of “votes”. Much more fitting would be: “if you vote with your wallet, people who spend more money get more votes”.
Of course this only applies if you’re talking about boycots etc, and not about buying stuff.
And yes, people with bigger wallets probably have more sway and power when it comes to get getting their way if they want to, but when people talk about voting with your wallet, they’re not talking about this.