If they are capable of constructing such a structure, they've obviously mastered the process of turning energy into matter. Planets are not enough to build what's required to create a structure of this size. First 8 light minutes away means you're talking orders of magnitude larger surface area than the star itself just for our star. The first 4 planets don't have enough metals to construct a basic shell big enough to create something to dim our star by 20%.
The most difficult part is to ensure the parts remain in place. The simplest way is thrusters, there you have a system that would be converting the solar output at 100% efficiency to eliminate the pressure, or providing a thruster for counter balance. It would make sense to start as a ring around the star and keep growing it equally towards the poles. Which if the light has steadily been decreasing, that makes perfect sense as the growth of the surface are of the sphere grows so should the dimming of the star happen.
I'd love to know how they deal with CME's.
Another alternative is a floating artificial planet that can move between systems that just drains the star of it's hydrogen and they convert that into what they need and/or they use that process as part of building the dyson sphere so when it's complete they have a dwarf type star left inside that's tame enough for them to deal with.