Datepicker flashes incorrect month when selecting a date range

When using two datepickers to select a date range, Changing a date one datepicker will cause it to flicker and briefly show the month currently selected by the other datepicker just before it fades out.

This issue can even be seen on the sample here: https://jqueryui.com/datepicker/#date-range

To re-create on the sample page:

1. Select the current date in the datepicker labeled "from". This indicates the start-of-range (I used October 26, 2015)

2. Select a date from a different month in the end-of-range datepicker labeled "to" (I used November 26, 2015)

3. Now go back and change the start-of-range ("from") datepicker to another date in the same month (October 25)

...As I make the selection in the "from" datepicker in step 3, It briefly switches to November (or whatever month the end-of-range is currently set to) just before it closes.

All functionality works fine, however this display issue is having a negative effect our users' experience.