I try to give an answer, welcome corrections!
When we write a state, we must notice the reference frame which the state lies in, because the form of state is diffrent in diffrent frame. Now I give 3 frames O,O′,O″. Their correlations are t′=t−τ′, t″=t−τ″, with τ′=−∞, τ″=+∞. Let's specify that the collision happens in t=0, in O frame's view.
When we say Ψ± are tranform as free particles, we actually mean Ψ+ transforms as free particles just in frame O′, and Ψ− transforms as free particles just in frame O″.
Turn now to the inner product between in and out states (Ψ−,Ψ+). Noticing that the product must be calculated in the same frame, we specify the frame is O. Now, we do a transformation T, and to see how the inner product changes. Please note, in frame O, neither of Ψ± transforms as free particles. However, we can use time translation to take Ψ+ to frame O′, and act on it with U0(T), then take back to frame O.
So, under transformation T, (Ψ−,Ψ+) changes into
(exp(+iH∞)U0(T)exp(−iH∞)Ψ−,exp(−iH∞)U0(T)exp(+iH∞)Ψ+)
Obviously, they are not equal, unless there are some restrictions on H.