If I understand correctly, those mirrors will reflect sun rays, that would otherwise be wasted across the universe, to earth.

So, you are fundamentally wrong. The very idea is to reflect sunlight that wouldn’t otherwise hit the planer. This WILL add extra energy to the planet.

Even if they used sunlight that bounces off earth, they would still cause issues, just a little less serious. This is because they would be trapping energy that tries to leave the earth.