Still under the eaves, though? Any windows or other openings this side of the house?
Some houses are pretty well closed off, others are totally vented so gasses under the eaves would go right into the attic. There, would cool and settle into the house.
Unlike cars with closed-loop fuel injection running 0 to 1 ppm CO, generators are carbureted and run rich, can produce very high CO. Recent ones have CO detector shutdown, but that only helps if operated in an enclosure.
Maybe if this generator is located where a permanently installed one would be, away from openings, it is OK. But at least examine the eaves for vents.