A usb drive will mount such that ownership and permissions will allow only you to access it. You may have created a samba share that allows everyone and your Aunt Tilly to access it but Linux permissions itself will stop it.
I have a a usb drive connected to a raspberry pi.
One way to work arounf this issus is to make everyone look like you - at least for these shares - by adding a line in /etc/samba/smb.conf:
Change edjski to your own Linux login user name
force user = edjski
You can put it within the share definition itself in smb.conf or you can add it to the [global] section - right under the workgroup line - to affect all shares.
Then restart samba:
sudo service smbd restart