Thank you for your patience.
Let me first start with the looking at the attached picture the RadTimePicker control is bound to a string property. My guess is that the SelectedDate property is bound to this string LatestFor property. The SelectedDate is a DateTime? object. Binding it to a string property will ignore the current applied culture format. I have tested this on my side and was able to reproduce it.
My recommendation is to bind the SelectedDate property to a DateTime? in order for the current date format to be applied.
var defaultDateTime = value;
_LatestFor = value;
Give this approach a try and let me know if it is applicable in your main application.
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