Enthelpic Excess Function - Phase Separation in Regular solutions

[elemis]

My professor, in his handout (picture below), says the following about this diagram :

For $\beta>+2$ there are two minima and phase separation occurs driven
by unfavourable enthalpic interactions.

I disagree with him partly. For $\Delta_{mix} G/nRT<0$ mixing is spontaneous and hence there solutions would be miscible. Hence at $\beta=2.5$ should we not expect the components to be fully miscible. ?

Following on from this logic; for $\beta=3$ the components are only miscible for $\Delta_{mix} G/nRT<0$ so the maxima represents a phase separation between the two components.

Who is correct ?

Additionally,the webpage below indicates that at the maxima there is one phase whilst at the minima there are two. Does this mean at the maxima the solutions are miscible ? If so, how can this be true given that $\Delta_{mix} G/nRT<0$ is positive and hence mixing is unfavourable ?

http://www.chm.bris.ac.uk/~chdms/Teaching/Chemical_Interactions/page_17.htm

 

[elemis]

Any ideas ?