The mixer is using tokens inside to avoid privacy leaks inferred from fees paid to miners during mix operations. So before you going into mixes, you’re buying enough mix tokens and then pay fees using them via fee-emission boxes ( Paying fee in ErgoMix in primary tokens ), with fee tokens equally distributed in outputs which is about approximate fairness. See ErgoMixer paper for details: https://eprint.iacr.org/2020/044
All the complexity is hidden in the application, end user do not know about fee tokens at all. And mixer dev (devs?) doing some profit by having a difference between token sell price and fee being paid later.