So I played Timmy all the way through all 4UC uniques coming online and a good amount of time using them, and it just felt really hard to keep up. I gave up because I was flanked by the two top civs in the game, both with over twice my score and defensive pacts with each other, and it was just too difficult to war them both. I even cheated in the Registan because by the time I unlocked it I had 21 population needed before I could build it, which was absolutely ridiculous. The extra culture per tech was barely enough to keep me 2 policies behind Egypt/Shoshone, both of which of course were directly next to me and constantly warring me.
I don't think the Tumen UU is strong enough, it doesn't have additional CS, just 1 movement, slightly less malus for attacking cities, and gold. It isn't terrible but for a civ that relies on razing cities to have any relevance it just doesn't do well enough at attacking cities. It ends up feeling like a kinda-sorta-slightly better unit, but civs like Ottomans and the Zulu get that kind of upgrade off of their UB while getting more off of the UU. And while the Deh and Registan+UNW are okay, they just can't carry a civ properly.
I'm not sure exactly what needs to be done to make Timmy relevant, but my feeling is that he gets online too weak too late. Your UA, UB, and UU don't come up until mid-game unless you have a lucky early game next to a non-early game civ. If you happen to spawn next to anyone that has strong early military (I was next to Aztec and Egypt), you just have to wait until so late that everyone is really far ahead, and your uniques don't offer a big enough power spike to catch up at that point. I also think a significant problem is that your UA scales up with conquered city pop and doesn't make up for how much you lose by just razing cities. The Moroccans for example get +1 per yield per trade route, not requiring war at all, but would also get the benefit of just holding on to cities while still keeping the trade route bonuses for a long time.