Judging by your pics, the stylist doesn't have a clue how to do Balayage.
It's tricky when you have to pay other hairdressers to do your hair. After a particularly disastrous cut, I always ask lots of questions before I let them start so I can be reasonably confident they know what they're doing.
In your shoes, I'd be asking exactly how they plan to rectify it before I let them loose for a second time.
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A few years ago, I worked in a salon where a rather over confident but still inexperienced stylist told a client 'yes, I can do an Ombre, no problem'. He'd never done it before and thought he could wing it.
I knew it was going to end in tears when he was so disorganised just setting up his trolley so I offered to assist but no, he knows what he's doing. I watched him from across the salon forget the order he was painting on several sections and the client ended up instead of a nice fade from dark to light, she had patches of pale blonde near her roots and dark tips.
I left the salon not long after that.