Direction belongs to the Lord: in a classroom the teacher's direction matters, not the students'. When you face a consecrated idol, all directions bow at the Lord's feet and become zero; direction is small and the Lord is great. So a small mandir on a study table may face East, and you sit before it facing North.
A temple in a wrong zone can be treated: merely correcting the deity's direction corrects one's condition. For a puja room in the SE, move a consecrated idol; if the idol is not consecrated there is no need to worry, as these rules are for consecrated idols. Paintings and decorative idols also represent planets and should be placed correctly.