You are confusing the Hans and Huns.
Both the early Tang and its predecessor Sui were for a time "tributary" states to the various Tujue tribes that grew powerful during 五胡 period (using Chinese history as a reference). Tang was an explicit vassal to "East Tujue" in its early days, until East Tujue itself felt again.
We won't discuss "Western Tujue", or prototype "Oghuz Turks" here.
There was this absolutely fascinating, if one might say "anti-China", "anti-Persia", and anti-a-lot-of-of-other-things pan-"turkist" history section as part of this website called "Ozturkler.com (or .org ..), until it was taken down a year or two ago. Ergo better not have done it or I'd be upset.
I learned many facts about "middle Chinese" history from that website than from any other source in recent memory.
If any Turks know if the site is "resurrected" in a different name or elsewhere - I just care about the history section, please inform and I would appreciate.
do you know that tang emperors were called "tengri khan"by the turks?