> but the parameter X1 only tells you what the predicted slope is for the reference group (controls),

No, the way you wrote the equation, X1 is for the entire group. You didn’t make a proper dummy variable.

    X1*age*isControl+X2*isControl+X3*isAutism+X4*isAutism*age+X5*age

This way you split out age effects for the two groups from what age effect is the same for both groups