Yes, your family member should have access to the storage space from your family account if he is listed as a member of the family group. However, it's possible that his OneDrive account is not connected to the family account. To check this, you can go to the OneDrive website and sign in with your Microsoft account. Then, click on the "People" tab and make sure that your family member is listed as a member of the family group.
Regarding his college student Microsoft email account, it's possible that he has a separate OneDrive account associated with that email address. If this is the case, he can link his college email account to the family account to access the additional storage space. He can do this by signing in to his OneDrive account with his college email address and then accepting the invitation to join the family group.
Note: You cannot use a Student email address with Microsoft 365 Family (not sure you were saying that)