Asking about finances for my cousin who just turned 18?

He does nothing.  That stuff between his ears will still  be oatmeal until at least age 21.  If he is very lucky she will not let him near that money until he is 25.

It's time for him to open his own account, and direct-deposit his earnings into that.  That will be a good exercise in saving and money management.  If he earned the money that is being held back, I agree that it should be his, but the sum should be insignificant compared to what he will earn and save as an adult.

If his foster mom put the money INTO the account, it's her money. If your cousin deposited the funds, it's HIS. However, proving that would cost more than the money would be worth. 

He should not be counting on getting this money. Her name was on the account, or she would not have been able to move it to another account--and I'm sorry to say that she did nothing illegal. It was mean, maybe--but not against the law. 

I'd tell your cousin to simply open his OWN account and start saving up to move out. 

You say that she opened an account for him, but you don’t say where the money in the account came from. If it was an account that she put money into on his behalf, he has no entitlement to it. 

Assuming that it's really still in the account and she hasn't spent it, he goes to court and has the judge order the bank to give it to him.

She controls it. He can pound sand.

Being 18 does not mean he is eligible for access a custodial bank account.

Most states have automatic transfer at 21. 

If your cousin is still living with his foster parents, I think he deals with it.  If he needs money for something specific he talks with his foster parents about it in a mature manner.

If he is living on his own, then it's his money and he should first talk to his foster parents and if that gets nowhere, discuss it with his caseworker. 

He exercises his rights as an adult. If the bank won't help he will have to take his foster mother to court if she won't relent.