Sorry to disillusion any of you but the muslim or qibla compass does not point to the east at all. The Qibla Compass points like any other compass to magnetic North-South nothing else. It comes however with preset indications/directions (depending on region), which points to Mecca and specifically to Ka'abah.

One of the earlier chinese compasses, the ladle or spoon compass aligned itself so the handle pointed south, yes, but then of course the other end will point to the north.

Compasses align themselves with the earth's magnetic field.
With the exception of gyro compasses which aren't magnetic at all and always point to true north.