[mthoms]

Yes, each salary is taxed normally. Then, there are laws against non-profit executives enriching themselves[0]. The government watches this very closely.

Also, public non-profits must release regular reports on their finances. So, contributors can decide for themselves whether the funds are being used appropriately. That's the basis for sites like https://www.charitynavigator.org [1] and https://www.guidestar.org

One particularly important metric is how much the organization spends on overhead vs how much is spent directly furthering their cause.

[0] Religious organizations seem to play by a different set of rules, but thats neither here nor there.

[1] A non-profit is not necessarily a charity, but this gives you an idea of how both can be evaluated.