The default behavior when the focus is inside an input control and it's Text is changed is that it's caret is placed in the beginning of the next text. This could be observed in the WPF TextBox control. In certain scenarios modifying the SearchText while the focus is inside the control is a desired behavior. In those scenarios the caret position is expected to be set to the end of the new text which is set to the SearchText property.
Attached to my comment you can find a workaround project for handling the input which is entered into the TextBox of the RadAutoCompleteBox. This sample project illustrates a scenario where any 'incorrect' input is not allowed. This approach was brought to our attention by one of our users which is why we send him special thanks.