The two things may be related but not necessarily. Since the water inside the toilet’s base is the only seal (in most cases) that prevents sewer gasses from entering your house, removing the toilet opens the sewer pipe / there’s no p-trap like under the sink, tub, or shower.
Removing the toilet opens the passage of air between the bathroom and a plumbing vent stack that should be terminating above the roof surface, that’s probably the draft he noticed while replacing the wax ring.
There are also TEE’s at the end of an inlet and dispersal pipes inside the septic tank (again, in most cases / depending on design) with their bottom ends submerged and top open for venting (picture below).
With a slightly open lid this could also create a draft, and yes, the cover should be closed and sealed, but mostly to prevent odors from escaping (gravity tank), and of course safety reasons.
Maintaining air pressure inside the tank is important in a pressurized system, the ones that include a pump.