It's a feudal event spawn Empire.
http://www.ckiiwiki.com/Hordes
I will add screenshots and version.txt when I am at home but I use the latest patch with the latest full and standard install of HIP.
Yes, we'll need that version.txt, and we'll need to know whether the Timurids _spawned_ or whether you started the game with them already active somehow (given their date of appearance, I'd think they'd have to have spawned).
What do you mean by "don't have imperial decay?" They should start with 0 Imperial Decay rating. Switching to them in-game, there should be a high-prio (up at the top of the intrigue menu) decision to Lower Imperial Decay. If that's there, they're subject to Imperial Decay as we would expect them to be. [If you hover over the decision, it'll show the current Imperial Decay rating even if 0.]
If that's not there, something may have gone wrong with their government type or something when they spawned. [E.g., maybe they spawned in the court of a nomad and thus improperly have nomadic government.]