Does the player have any idea about the backstory of their PC, family etc, or have they just decided they want to play a tiefling and haven't thought much beyond that yet? I'm not a Dragonlance lore guru, but there doesn't seem to be any obvious lore space for large numbers of tieflings, or tieflings as a widely-known species.
The way i'd do it personally is to say that somewhere in the distant past, one of the PCs evil ancestors made a deal with a fiend of some sort, and the fiend has maintained a connection with the family line ever since. Sort of a family demon, a bit like a guardian angel except ... not. Sometimes the family produces fiend warlocks, and maybe sometimes a child is born that has been tainted by the fiend's proximity and is basically a tiefling. the family could be corrupt nobility or insular pig farmers, anything clannish and insular. And there might be less backlash, angry mobs etc than you'd expect, too. Remember that Raistlin ran around for 6+ books with hourglass-shaped pupils and metallic-looking skin, and I can't remember any of the strangers he met commenting on it. Presumably a tiefling would be treated similarly.