Should the aspheric surface of an asphere always face the object / light source?

In most cases, yes. Aspheres are typically designed so that the aspheric surface faces the object, or a collimated light source. This helps to spread the refraction, or bending, of light between the two surfaces of the lens and minimize spherical aberration. However, Best Form Aspheric Lenses are designed in the opposite configuration, so that a planar surface faces the object or collimated incident light. These types of lenses are simpler to design and achieve diffraction-limited focused spots on-axis for a given wavelength, but changing wavelengths result in chromatic aberrations and reduced performance for wavelengths different than the design wavelength.

Also, back reflections of light incident on the planar surface of best form aspheres bounce back directly towards the light source. This can be a cause for concern in many laser applications, making best form aspheres unsuited for some laser systems.