The RadTimePicker control exposes the following server-side events:
ChildrenCreated occurs when the child controls (the input area, popup buttons, and embedded calendar or time view controls) are created.
SelectedDateChanged occurs when the user changes the value of the control, either when input area loses focus after the user has typed a new value, or when the user selects a new value in the popup calendar or time view control. This event does not fire unless the AutoPostBack property is True (RadDatePicker, RadTimePicker and RadMonthYearPicker) or the AutoPostBackControl property is not "None" (RadDateTimePicker).
ItemCreated occurs when an item in the time view is created.
ItemDataBound occurs when an item in the time view is data bound.
In order for the server-side events to be invoked the RadTimePicker control needs to perform postback. In order to do this you should set the AutoPostBack property of the control to true.