Privatebanker is giving the legal definition of a joint account. Both parties own 100% of the account. That doesn’t mean there is double the amount in the account, just that each owns 100%. Legally the money in a joint account isn’t partly yours or your mother’s, it’s all yours and all hers. The bank doesn’t hold it separately and doesn’t care who deposits money -either can take it out.
The IRS only expects one of you to report the interest, but it would happily garnish the entire account to cover a tax bill and you would have a claim against the other party for your portion. The bank doesn’t want to be involved, just like it doesn’t want to be involved when one sibling takes all Mom’s money and the siblings say 'But Mom said you would share!" The law says the bank can pay the entire amount to the joint account holder and the sibling are SOL.
FAFSA reporting doesn’t go looking for accounts. YOU report them. If you feel the money in the account was reported correctly, then you’re okay.