The Society hasn't been consistent on this subject. The 1969 book Is the Bible Really the World of God, in an apologetic attempt to explain how the Flood waters covered the entire earth, argued that mountains like the Himalayas and the deep ocean basins did not exist until after the Flood (pp. 36-39), with the major geological changes occurring in the year that the Flood waters "receded". But then the 22 June 1977 Awake! had an article that summarized the major evidences and ideas of plate tectonics and presented it as a feasible, though not proven, theory. Yet the old catastrophic explanation of how the Flood could have covered the earth was still commonly used (Insight, 1988, Volume 1, p. 610), and the presence of marine fossils at the top of Himalayan peaks is also used as evidence of the Flood rather than plate tectonics lifting the seafloor upward (Did Life Get Here By Evolution of Creation, 1985, p. 203). More recently, Ciro Aulicino in his talk "You Will Be With Me in Paradise" made explicit mention of continental drift occurring catastrophically during the Flood:
"Jehovah God can direct the cataclysmic forces at Armageddon to rejoin — now notice my word, I'm not saying join — to rejoin all the land masses as they once were before the Flood. And scientists tell us that is the study of Pangaea, which is at one time the earth was one complete connected land mass. It was in the Awake! magazine too. If you want to look it up on your new CD-ROMs, brothers, just press the button and you'll find it there. Connecting the Americas to Asia through the Aleutian chain, linking Europe through Britain to Canada, Australia to Asia via the Indonesian archipelago, and raising land corriders to island groups in the Pacific and the Carribean. Now why we cannot be dogmatic about all this, one thing is certain, friends. The topography of our earth will be changed, as it did under the heavy floodwaters of Noah's day. Remember, it was all connected and then it was all broken up. In fact friends, did you know that Jehovah used the Deluge's water to form the continents as we know them today?" (audio)
The notion of "hyper plate tectonics" is purely motivated by religious beliefs, not by anything one could actually learn from science. It would seem that in reality, the JWs are "young earth creationists" after all. The planet is admitted as billions of years old but any actual geological history is strictly located within the very recent past, or else how would the Flood waters cover the tallest mountains? The uplifting of mountains and the subduction of plates down trenches is placed within a year's time, as these are necessary for the waters to cover land globally at the beginning of the year and for the waters to drain off land at the end of the year.
To put things into perspective, the 2004 Indian Ocean earthquake was the third most powerful quake ever recorded, 9.1. It produced the most devastating tsunami in recorded history. The plate shifted about 20 meters in this event. That's it. How long does it take a person to walk 20 meters? "Hyper plate tectonics" on the other hand would require plates moving thousands of miles very quickly; the northward movement of the Indian Plate, for instance, closed up part of the Tethys Sea and uplifted the seafloor. This would have, say, the Indian subcontinent move countless times faster than the spreading seafloor could be laid down at the central and southeast Indian mid-ocean ridges. That seafloor in general was laid gradually, of course, can be observed in the record of magnetic field directions in the oxides in the rock, the long string of seamounts, atolls, and islands formed by the mid-Pacific hotspot which show a long-term geologic cycle, the seasonal weathering of uplifted rock (such as the Alps which are worn down as quickly as they are lifted up, largely through spring meltwater from the snowpack), the geologic record of rivers changing courses many times, etc. The rate of uplift of the Himalayas would have to be much higher than is apparent at first glance since one would need to factor in erosion. According to surveys of the Himalayan plateau, a total of 5-9 km of rock was eroded from the Tibetan Himalayas and about 12-25 km from the Higher Himalayas, which produced the many foothills and smaller ranges to the south. Compare these figures with the height of Mount Everest, which is only 8.8 km in height. So the height equivalent of one or two Mount Everests have been eroded away throughout the whole plateau as the Himalayas were pushed up. And considering that under normal monsoonal conditions 2.9 mm is eroded away per year, it would take millions of years of weathering to accomplish this feat.