A runtime only user would have no purpose in getting into the back-end. There should be only one entry point for such a user, the front-end, where menus will lead them through their available processes.
I have to question your initial statement, "I have successfully split a database I created ". Are you saying that you can run forms, queries, and reports successfully after splitting the database? If so, you need install only the front-end on the other workstations (unless you intend for everyone to have their own private copy of the back-end data).
After you have installed the front-end on another workstation, is that workstation able to run any forms, queries or reports? If not, it could be that your back-end has not been placed in a network resource available to everyone.
Jim