I think it's more complicated than that.
Tillerson felt alienated and resented Trump. Trump resented Tillerson for contradicting him over and over again in public.
If you watched Tillersons press conf. today you saw a defeated man almost in tears. You can't exactly blame Trump he warned him multiple times but you could tell Rex was completely humiliated.
Just a few points on what drove a wedge between them.
-Tillerson lost autonomy to pick ambassadors.
-Kushner was handling diplomatic missions historically reserved for the sec of state.
-on top of losing autonomy to pick ambassadors, nominations have never taken this long in history which marginalizes the state dept.
-They disagreed on some key policy positions.