All I can offer is what I've read and my opinion. I would not count on good expansion from TTSX below 2000 fps. In fact, I would prefer 2200 fps or greater. In the links that I posted, the experiments indicate that the key factor is actually energy, which is certainly related to velocity, but not the same. He found that heavier TTSX expanded at lower velocity because they had more energy. However, the key variable is which cartridge did Barnes have in mind when they developed the bullet. He was testing .277 bullets. The lighter weight bullets are geared toward the lower velocities of 6.8mm SPC while the heavier bullets are designed for the higher velocity of the .270 win.
In his testing, the 85 gr TSX, 95 gr TTSX and 110 gr TSX all expanded quite well at 1300 ft-lbs of energy at impact. The 130 grain (clearly intended for the faster 270 win) needed nearly 2000 ft-lbs to achieve full expansion.
My guess is the 150 gr .30 cal TTSX is designed with the expectation that it will be used in .30-06 and even .300WM and will require significant energy to expand. That's the bullet I'm shooting in my .300WM. The 130 is probably a better bet for the lower velocities of the .308 win. Heck, I'd try the 130 gr in my .300WM.
Edited to add: Looking at the Barnes factory ammo I see that the 150 gr bullet is offered in .300WM and .300WSM, so the bullet is designed to work at much higher velocities than the .308 win produces. The 130 gr is not offered in the magnums, so it is intended for .308 win.