I do not use the same "sort" setting in both views:
When switching bewteen these 2 tabs (from one tab to the other, whatever the "from" and the "to" are), I need to have the display manually forced refreshed (F5 for me) to get properly displayed list (i.e. according to sorting criteria for this specific view).
Otherwise, by default, the "to" tab (i.e. the one to which I did went to) is sorted with the sort criteria defined for the "from" tab (i.e. the one in which I was).
I would expect that a click on the another tab (= to have the view of this tab activated as the active display) would force a refresh of the contents just before displaying it.
According to my tests, this is not the case (i.e. if it is programmed like this, the result is not what it is expected)
So, to document my explanantion: