That's correct.
When you right click on a folder, usually you have 4 tabs: General - Share - Security - Personalize (or customize, I can't remember right now).
You just set the permissions on SHARE, which is correct. Now you have to click on SECURITY > Advanced > Edit > here you should find a check mark on "Include inheritable permissions from ........." uncheck this box and click on COPY. This may take a while depending on how many files you have on that folder.
Once done, from the same screen, click ADD...
You will see a mask where you can put a name, write the username you want to grant, let's say User1. Then click Check Names and the name you just wrote, should be underlined.
Click OK, on the next screen tick FULL CONTROL, this will activate everything. Before clicking on OK, be sure to remove the tick from "DELETE", "CHANGE PERMISSIONS" and "TAKE OWNERSHIP". Click OK. Now continue to click OK until every mask disappear.
Now you should be able to access your folder from another computer by typing: user1@mydomain.com and its password.
Let me know.