By default, the DisplayOwneLevel property is True. The OwnerLabel property indicates the label being displayed in the time unit, once it gets magnified. Use the AllowInsideFormat property to avoid displaying the inside units, and so the inside labels. The InsideLabel property defines the label for inside units being displayed. Use the SplitBaseLevel property specifies whether the chart's base level gets divided when inside zoom are shown.

The following screen shot shows the unit with DisplayOwnerLabel property is True ( The Jun 24 is getting displayed on the first line, while the second line displays hours ): 

while the next screen shot shows the unit with DisplayOwnerLabel property is False  ( The Jun 24 is not displayed, and actually only hours are displayed ):