I just purchased a Minecraft Java account for my son on our home computer. My step-son has an account that was purchased at his mother's house that he accesses on our computer when he is with us. When I attempt to access Minecraft for my son (separate email address, different username) my step-son's worlds show up. How do I get it so my son can access his own worlds?
Minecraft uses a single instance, worlds aren't seperated by account, any person logging in can use any world on that instance.
You can use a tool like http://multimc.org/ to create different instances of Minecraft avoiding this problem (each person logs in to their own instance and has only their own maps).
By default, Minecraft uses one folder to store the data for all profiles. However, you can change that with the default launcher. (note that "Profile" and "Account" are not the same thing)
Set up a profile for each of them using the "New Profile" button. You can change the game directory for each profile in the "Edit Profile" menu. Setting a different game directory for each profile will separate the save files.
Note that this will not separate saves by account, but by launcher profile, which can be selected individually on the bottom right hand corner of the launcher.