As a general guide, I'd say it isn't worth the trouble and that resistance/immunity should be applied to secondary effects, as well.
In the specific case of a tiefling, they only have resistance. That's half damage, which can be described/justified any way the group feels appropriate. Maybe it means that the tiefling only marginally effected by the temperature at which a house would burn, but has trouble with the smoke, etc. It could also mean that their system is adapted to be able to process the ash and smoke from a burning landscape to the same extent to which they can deal with the heat.
For immunity, well, we're talking about dragons, demons, devils, golems, and other critters that pretty well defy biology and other assorted fields of science. Don't overthink it. It would be really super lame for a glabrezu to stride through a fire with a smirk on his face, only to step into an eddy and gasp for breath.
I know it's glib, but I'd say that it's just a game. Don't sweat the small stuff. Unless you're doing something truly unique (i.e. you'll only need to worry about the ruling once, ever, for your whole life) with a given scenario, this is truly small stuff. Fire damage includes whatever is going on with the flaming whatever.
That said, some people want to sweat the small stuff. D&D isn't designed to do that. If this bothers you, there is enough hand-waving around other small stuff that you're going to go insane. Either switch systems (though I don't know of any that would actually consider this sort of question worth addressing -- maybe Fate, depending on how you want to handle aspects) or lower your bar and accept the system for what it is.
Note that I'm talking just about the secondary effects of a burning house. If you want to put pods in that release poison spores or something similar, knock yourself out and welcome to the Evil GM Club. Your card is in the mail.