What version of FileMaker are you using?
If FileMaker 12 or 13, there is a script trigger specific to changing panels that you would normally use for this instead of OnObjectModify.
A key difference between different triggers is whether the trigger is tripped before or after the triggering event is processed. OnObjectModify processes the event (changing tab panels) before tripping the trigger. Thus, Exit Script [False] has no effect on whether or not the tab panel change takes place.
But OnPanelSwitch (name is different in version 12) is tripped before the triggering event is processed and thus Exit Script [False] can cancel out the panel change when this trigger is used.
Then I recommend that you use OnPanelSwitch instead of OnObjectModify for the reasons listed above.