HG, yes the WTS now teaches that the judging of the sheep and goats does not start until the great tribulation (future) starts.
*** w00 1/15 p. 13 "Keep on the Watch" ***In the parable of the sheep and the goats, the Son of man arrives in his glory in the period of the great tribulation and sits in judgment. He judges people on the basis of whether they gave support to Christ’s anointed brothers. This standard for judgment would be meaningless if at the time of judgment, all of Christ’s brothers had long since left the earthly scene.—Matthew 25:31-46.
*** w03 12/15 p. 15 par. 8 Our Watchfulness Takes On Greater Urgency ***In modern times, sincere students of the Bible have learned from the inspired Scriptures that this system is doomed to destruction. Do we believe this? Notice what Jesus Christ clearly stated: "There will be great tribulation such as has not occurred since the world’s beginning until now, no, nor will occur again." (Matthew 24:21) Jesus also said that he would come as God’s appointed Judge and would separate people as a shepherd separates sheep from goats. Those found unworthy would "depart into everlasting cutting-off, but the righteous ones into everlasting life."—Matthew 25:31-33, 46.
*** w95 10/15 pp. 27-28 par. 21 What Future for the Sheep and the Goats? ***What, though, does this fresh understanding of the parable of the sheep and the goats mean to us? Well, people are already taking sides. Some are on ‘the broad road leading off into destruction,’ while others try to stay on ‘the cramped road leading off into life.’ (Matthew 7:13, 14) But the time when Jesus will pronounce final judgment on the sheep and the goats depicted in the parable is yet ahead. When the Son of man comes in the role of Judge, he will determine that many true Christians—actually "a great crowd" of dedicated sheep—will qualify to pass through the final part of "the great tribulation" into the new world. That prospect should now be a source of joy. (Revelation 7:9, 14) On the other hand, vast numbers out of "all the nations" will have proved themselves to be like stubborn goats. They "will depart into everlasting cutting-off." What a relief for the earth!