In the debugger tool, after you select a date, use the inspect button and select the date picker to see if the value is what had been selected.

Also, when you want to press the button to save the data, in the inspector tool, first click step by step, and then click next step until you get to the save data step and inspect the values being sent to the database to verify the date is being sent.

Also, check in your logs to see what date value was sent.