Amongst the Orthodox, you don’t really hear talk of private revelations. A few have been elevated through the centuries (e.g. the Protection of the Theotokos), but they are blessed few. And no one ever talks about how they are waiting for the bishop or synod or whatever to declare something legitimate.
For the most part, Eastern literature says something to the effect of, “Distrust anything too out of the ordinary, because you might be deluded.” But both patristics and modern lives of the saints include stories of visions or apparitions or what have you, so I guess folk piety and the test of time (as well as generous hagiographers) play into if something is accepted.
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