Double Wall Pipe Connecting with Single Wall adapter at Ceiling????

[CH123456789]

Hey

Any help would be very much appreciated. My installer just left and I noticed this.

1. Double wall going from stove to ceiling support but at ceiling support connect a single wall snap lock connection is used?
2. Wont all the hot air in the double wall insulation cavity terminate at the ceiling support box and get very hot right there?
3. Where does the air in the insulation cavity normally go. Does it continue into the insulated cavity of the chimney where it is supposed to meet in the box?

Thank you