A dry chair under an upstairs deck sounds like an excellent use of the space. The ceiling is the visible purchase. The water route is the purchase that makes the chair usable.
Decide where the water will travel
Ask the installer to show the collection surface, slope, seams, downspout, and discharge point. Follow that route all the way into the garden. A system that moves the drip onto the basement entrance has merely relocated the problem.
Trex RainEscape's installation resources illustrate an above-joist system installed as part of the deck assembly. Retrofitting that kind of system can involve lifting boards. Compare actual product details rather than assuming every under-deck product installs from below.
Keep the ceiling repairable
Lighting, wiring, and access panels should be coordinated before the ceiling closes. Ask how a leaking joint or blocked outlet will be reached later. The answer should not begin with removing the entire finished surface.
Compare quotes at the same boundary
- Is removal and reinstatement of existing decking included?
- Are wall junctions and posts shown in the drainage detail?
- Where does the collected water discharge?
- Who handles electrical work and verifies suitable fixtures?
- Can the ceiling be opened without destroying the drainage layer?
Wind-driven rain can still reach an open-sided outdoor space. Keep that distinction in the furniture choice and storage plan. This is a sheltered outdoor room, unless a separately designed enclosure says otherwise. It does not become indoor storage because the ceiling looks finished.