That seems like magic given the 3100lb curb weight. I guess with the right gearing and of course the paddle shifters, but still... I'm not sure how that's being done.
If you just sat me down and said "3100lbs, 3.8s to 60, estimate a horsepower", I'd have said like 500. Sure, put that engine in an elise and you can get your times down there. My intuition is not properly calibrated here.
Edit:
It's not even the high 300s... this is E46 M3 territory in terms of HP and weight (ish).
The biggest difference between your frame of reference (E46 M3) is the MASSIVE advancements in tire technology and gearboxes. The Supra is geared extremely aggressively, because it can be, because it has 8 forward ratios. Also, while it may be "only" 335hp, it has a very sizeable amount of torque and its available on a broad plateau. Couple that with the fast-shifting 8 speed auto...and 3.8 sounds believable to me.
edit:
E46 M3 weighs 3460lbs. It makes 338hp, 269lbs*ft, and the total torque multiplication for the first 3 ratios are: 15.31, 9.16, and 6.04. So according to my theory that what you "feel" when accelerating is really the multiplied-torque to weight ratio, the E46 has:
4118lbs*ft / 3460lbs = 1.19lbs*ft / lbs in first gear
2464lbs*ft / 3460lbs = 0.71lbs*ft / lbs in second gear
1624lbs*ft / 3460lbs = 0.47lbs*ft / lbs in third gear
A90 Supra weighs ~3400lbs. It makes 335hp, 365lbs*ft, and the total torque multiplication for the first 3 ratios are:
16.58, 10.60, and 6.85. ...
6051lbs*ft / 3400lbs = 1.75lbs*ft / lbs in first gear
3869lbs*ft / 3400lbs = 1.13lbs*ft / lbs in second gear
2500lbs*ft / 3400lbs = 0.75lbs*ft / lbs in third gear
As you can see, the A90 Supra should pull very nearly as hard in 2nd gear as the E46 M3 does in
first. Lighter, a lot more torque, more aggressive gearing, and much faster shift times. Add launch control to the mix and I can see how the Supra is quite fast.