The Turner Mansion is the home of the Turners in an alternate Universe where the Turners are rich.
It is the home of the Turners in an alternate universe. It was created after Timmy wished that his great great grandfather, Ebeneezer Turner, chose Railroad Tycoon instead of Town Crier. This made the Turners rich.
Both the exterior and the interior is similar to that of the Buxaplenty Mansion in the main universe. It is possible that this is intentional, as in the alternate universe, the Turners essentially filled the Buxaplenty's shoes, being the richest family in town.