To fix the start time of a clip in the playlist:
Right-click on the clip row and select Properties.
In the Fixed-time tab, specify the start time parameters.
The settings in this tab have a higher priority than the default ones in Settings menu > Fixed-time event.
Click OK to apply.

NOTE: The default start tolerances are 10 seconds earlier and 30 seconds later! If you want to change them, go to Settings menu > Fixed-time event, or use the Custom tolerances spin-box in Clip properties > Fixed-time tab.
WARNING! When using fixed start times in a daily playlist, the total time of the playlist should not go beyond midnight!