How Does DayBack Show Conflicts
The calendar "shows" conflicts, instead of preventing them. So you'll be able to see that two events overlap for a given resource or a given date / time.
If you want to enforce the prevention of conflicts--or show dialogs when they occur--you'd do that in FileMaker, writing a script that searches for conflicts for the current record and then running your new script from within the script "Create Edit Delete Event..." that DayBack uses to manipulate events.
We've put together an example script that does this for you. See how it works and find instructions for adding it to your copy of DayBack here: show conflicts script.
Show Events Side-By-Side Instead of Overlapping
If you'd like your concurrent events to appear side-by-side rather than overlapping, you can modify the "Load Calendar Settings - On Startup..." script to do just that.
Under the comment '# Would you like to prevent events from overlapping' change the variable in the next line to True. For example:
'Set Variable [$$sc_PreventEventOverlap; Value: True //...'
After you've made the change, run the Upon Opening script and you should see your concurrent events displayed as desired.