When you change these settings in the CPanel, as you noted, the setting is strictly enforced for all users in the Google Apps instance. The user no longer even has the ability to share Drive files outside of the domain.
There are no API settings that correspond to the CPanel settings. The way FlashPanel appears to be enforcing the settings is by setting up "rules" (this OU can't share with people outside the domain except for this external domain). Then FlashPanel monitors user file sharing under that OU, looks for violations and can either automatically undo the share or send a notification of the violation.
Thus FlashPanel is not strictly enforcing the sharing policies like the CPanel setting can. The user still has the option to share externally and for some period of time, the file is actually shared externally. FlashPanel simply has the ability to notifiy and or rectify the situation afterwards.