You didn't state what method you are using to create the samba shares - there are 2: One is created in Nautilus and the other is in smb.conf itself.
I'm guessing that had you used Nautilus it would be obvious since you would have checked only 2 of the 3 boxes to make a private share ( see attachment ).
To create a private share in smb.conf in it's simplest form:
Note: There are an infinite number of variations of that type of share definition depending on how you want to control who can do what.
path = /path/to/folder
guest ok = no
read only = no
In either method you will need to create a user on your Linux box representing each LAN user and then you have to add them to the samba password database. So if you have a remote user named morbius:
** Create a user morbius on your Linux box.
** Add him to the samba database using this command:
sudo smbpasswd -a morbius