If the Mixer has little BTC or is new they might not have funds on another chain to send to you and then they just forward your BTC back to you which has the same trail.
If the mixer have little BTC, they shouldn't open their service in first place or at least mention limit of deposit amount. If you can't trust mixer to do it's job correctly or actually erase user data, you should seek alternative way to protect your privacy such as CoinJoin.
absolute privacy requires the use of a decentralized mixer that does not collect user data.
Absolute privacy is impossible.