physical chemistry - Why will A atoms diffuse from β phase to α phase and B atoms from α phase to β phase?

At the initial compositions 1 and 2 of $α$ and $β$ respectively the chemical potentials of A and B atoms in each phase can be found by extrapolation of the tangents to the free energy curves at 1 and 2 to the corresponding sides of the free energy diagram, as shown above.

All atoms diffuse so as to reduce their chemical potential. Therefore, A atoms will have a tendency to diffuse from $α$ to $β$ $(μ_\ce{A}^α > μ_\ce{A}^β)$ and B atoms will have a tendency to diffuse from $β$ to $α$ $(μ_\ce{B}^β > μ_\ce{B}^α)$

The point marked 1 and 2 are basically the compositions of two metal alloys that have been welded. Now annealing is performed at a particular temperature $T_1$ to bring about the change now why will A atoms diffuse from $\beta$ phase to $\alpha$ phase and B atoms from $\alpha$ phase to $\beta$ phase?

How will drawing a common tangent be different in interpretation than drawing two individual tangents at compositions 1 and 2?