The initial concerns from Patch 10.1.5 PTR were invalid and the catch-up gear from Time Rifts works with the Revival Catalyst on live servers!
Initially, this was not the case and the item level 402 gear offered by the vendor in Tyrhold Reservoir could not be converted into tier set items, as shown in MrGM’s tweet.
However, Blizzard have changed their mind and you can now convert the catch-up gear using the Catalyst. Courtesy of soulsobreezy.