One Employee Taking All Tips

Hello! I just got a new job at a cafe. I work with one other person making coffee and serving pastries to customers. The main person I work with is a middle-aged woman who has been there for a few years. When I was first hired I was told that I'd be making $16/hour plus about $50 in tips per day. I was told I wouldn't be making tips during my training week and I thought that was reasonable, but I'm now done with the training.
I was recently told that the woman I work with takes home all of the tips made during her shift, without pooling them, because of a deal she made with the owner. He supplements this by giving me a $20 bill out of his pocket at the end of the day, but it's nowhere near what I'd be making with tips (I watched her take home $120 from one shift, meaning I actually would've made close to $60). On days that she doesn't work, all of the employees pool tips. She's also very mean :(
Is this allowed? I'm thinking of quitting.
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