Just make sure your finder isn't set to run on startup. Thats the easiest work around. You could do a lot of things like Automator, AppleScript etc, but just set your Finder menu to not populate on start up.
I can't duplicate your error.
Note : Finder will always take precedence when it's open the first time.
Go to System Preferences > Users & Groups > Login Items and make sure Finder isn't there. If it is delete it. Also, Relaunch Finder, could be in there. If it is, delete it.
Make sure none of the applications that you want to display are set to hidden.
If neither are there its an OS glitch.
Open Application> Utilities> Disk Utility> Select Macintosh HD> First Aid> Verify Disk Permissions> (when done) Repair Disk Permissions
Restart your system
Additionally, when you restart or shutdown if the box below is checked and Finder window is currently open then it will naturally reopen upon restart. Make sure all windows are closed or the box is not checked if necessary.
If that does not work a clean OS install would correct your issue.
If your asking how to make an application show on log in and show Finder window on login too but make the application fullscreen you can not do that without some scripting or automator process.