However I believe that the Orthodox still have the same teaching that she was assumed into Heaven.
This is true, although we know that the belief in the dormition is certifiably older across the church than belief in the assumption (which was a local belief for a long time).
But we do not believe it because the Pope said so. In fact to a great extent, the Pope only could say so because it has been our traditional belief and he could reach back into early church history for evidence of this belief, of which Orthodox have a treasured memory. If he had firmly declared the opposite opinion we would still believe it and still ignore him.
To clarify, Orthodox do not recognize the Pope’s right to make the proclamation, because no single bishop anywhere has that right. It does not matter that he happens to agree with us in this instance.
Which brings me to another point. Perhaps he felt a compulsion to make the declaration because Latin Catholic belief in the idea was waning. Why should it? What is so different about the Latin church that it needs these fiats from the Pope?
I can only speculate here but I think it might have something to do with the scholastic tradition of the western church, which began as a scholarly revisiting of the ancient faith and encouraged educated Catholics to think that higher illumination was possible over time, given enough study and reflection. This leaves the church open to all kinds of rationalization, even to explaining away embarrassing paradoxes.
For instance, in this case the modern world (1950’s) had reached an age where contemplating space travel was actually possible (the United States and Russia were in a space race within a decade). Powerful telescopes and other measuring devices had clearly shown that there is no heaven in the classic sense anywhere closer than Jupiter, at least in any observable form. So scientifically one could legitimately ask “what happened to this body?..did it’s internal pressure cause it to explode in the vacuum of space?”
So if modern theologians attempted to explain away this paradox with scientifically based and philosophically based logic, they would be working in the scholastic tradition. They might come up with an elaborate scheme explaining why the body did not explode, or which direction it might have sped off of a globe spinning at 600 miles per hour. Or they could have resorted to the notion that the “belief” as such was just a metaphor for something else, or a legend constructed by a more primitively rustic and unsophisticated age that can be dismissed as early fantasy.
Thus, a perceived need to act, reassuring the conservative and the middle of the church membership, while tending to push the skeptics out.
Orthodox did not have this type of problem, at least not as bad. Perhaps (as has been declared by some) the rank and file in Holy Orthodoxy are a bit more rustic overall

but Holy Orthodoxy is much more comfortable with paradox, not feeling as much need to explain it all away. The dormition happened, and the assumption followed, that’s all we need to know.
Also, there is no big party in Holy Orthodoxy vested heavily in this idea, their faith does not rise nor fall on it so no one subgroup feels particularly threatened.
Michael