Hi and welcome to the Forum!
I don't know why you would have to set your time in the future, I've never heard of this being a fix for anything. But I would try deleting your settings in both iMessage and FaceTime then reset your iPad and then reactivate both these apps.
Reset - Hold the power off button and the home button simultaneously, keep holding them in and you will see the power off slide appear and disappear, wait until you see the Apple logo appear before releasing the buttons. It will take a little longer for your iPad to start. Let us know if this makes a difference.
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How do I delete my settings from FaceTime and iMessage?