I have gone through several links about the dot convention of mutual inductance, but nowhere could I find the reason why a dot is placed where it's placed. Is it to do with any direction of current and field or some other reason I cannot understand? Can anyone elaborate on the physics behind the dot position?
You can understand this from the Transformer page on Hyperphysics.
To summarize, the direction of the magnetic field through the core depends on the direction the primary wire is wound around the core.
Similarly, the direction of the secondary EMF depends on the direction of the magnetic field and the direction of the secondary wire is wound around the core.
In this image (from Hyperphysics), the dots would both be placed on the upper side (or both on the lower side) of the coils, but be careful to notice the direction of the windings:
This analysis is derived from Faraday's Law of induction