Tried replacing brake pads for the first time - Shimano Tiagra Caliper on road bike. Unscrewed the small screws that held the pads in place, slid them out and slide in the new ones. Tighten the screw. Then I noticed when I squeezed the brake lever tight, the pads are not perfectly parallel to the rim. When seen from above, I can see the back side of the pad touching the rim, then hairlines towards the front with a <1mm gap. the brake pad is not fully engaged with the rim.

I checked to see whether the brake pad was slide in correctly. It seems so since I can see the interlocking hook between the back side of the pad/shoe locking together correctly. I tried squeezing the brake tight against the rim before I tightened the single screw that holds the shoe in place. But when I release the brake lever, the shoe "bounces" back into the non-parallel condition. I also tried adjusting the brake cable length. Nothing helps. The brake shoes on both sides have the same symptom. This happens only on the rear brakes, the front seems OK.

Aside from the screw that holds the shoe in place, I don't see any adjustment I could make to modify the "tilt" (what is the correct term to describe this?) Should I be concerned? Or should I just wait until the pad wear out to such a point that the surface is parallel to the rim?