If I printed a target then stacked it on red paper, would the red show when a shot was fired?
The bullet is going to penetrate both the target and the red paper, so at most, you're only going to see flecks of the red peeking through the hole.
You can get reactive targets, like the ones made by "Shoot-N-C". These have a black layer over a colored layer. When hit by a bullet, some of the black layer surrounding the bullet hole flakes off, exposing the colored layer underneath: