Well, it seems that virtually all of the nomad steppe people were quite good at the 'Parthian Shot' kind of tactics, and all these peoples shared these skills since very early days as with the Scythians, all the way up to the cossacks of near modern history. Use of a bow was vital for survival in the open steppe. But you bring up an interesting question, just what did cause the explosion of Mongol expansion?

From what I know, I guess one ambitious tribal leader with a slightly over populated tribe got ambitious, started consolidating all nearby tribes and the rest is history. But why not sooner?

I don't think the Mongols had many cataphract (heavy armored cavlary) units, though I could be wrong. I am sure they had some guard units with heavy armor, but it seems the vast majority were the typical medium armored cavalry rider as described in that link you gave.