You need to do the inverse transform back into object space of intersection points.
Incrementally build up the inverse transformation matrix as you incrementally build the current transform matrix.
Pseudo-code for display procedure looks like (skipping over some details):
for each pixel
form ray
for each object
inverse transform ray (source point and direction) into object space
if (intersection of ray and object exists)
if (closest intersection so far)
transform point and normal back into world space
record object, object space point, world point, world normal
if closest object is textured
get texture color from object, texture and object space point
do illumination model using color, world point, world normal
record pixel color