It is usually best when the plastic backer is not tightly or rigidly attached to the back of the aluminum face. That is why faces for lighted signs are never rigidly attached to sign cabinets, but float in retainers or are suspended from hanging bars—both methods allow the plastic to float and move without being distorted.
Standard practice for routered faces has traditionally been to stud-mount the plastic backers, hanging the plastic from 10-24 studs spot-welded to the backs of the aluminum faces. The size of holes in the plastic to receive the studs should be at least double the diameter of the studs. Drill the holes in the plastic first, then use the holes to mark the aluminum for studding. Try to center the studs so they locate in the middles of the holes. Nuts on the studs should be finger tightened only. Speed nuts work well. Also, 3/16-inch plastic will stay flatter than 1/8-inch and will require fewer studs.
Stud-mounting will guarantee there will be no failures. On the other hand, failures are not uncommon where adhesive only, or adhesive/tape is used.
If you are willing to do repairs, you may decide to use an adhesive-only mount, as it is quick and easy, but it is good to make the back of the face easily accessible when building the cabinet to minimize future repair time. There is nothing more frustrating than having an expensive routered sign with plastic backers falling away from the face on the inside and not being able to remove the plastic without great difficulty.
Also, note that a rigid adhesive will fail before a soft adhesive will, because of the dissimilar expansion rates, as a rigid glue does not allow the plastic much movement and more stress is placed on the bond.
Really, an investment in a stud welder is well worth the money, in my opinion, and will pay for itself in eliminating this problem almost entirely.
Brad in Kansas City