Internal Energy Changes in Adiabatic Reactor
You omitted the energenics associated with breaking chemical bonds and making new chemical bonds.  If this contributes a negative change to the internal energy (exothermic reaction), then the temperature would have to rise to offset this effect so that the overall change in internal energy would be zero.  If it contributes a positive change to the internal energy (endothermic reaction), then the temperature would have to drop to offset this effect so that the overall change in internal energy would be zero.  Saying this in a different way, when you have a chemical reaction occurring, the internal energy can change even if the temperature is held constant.