The first incorrect assumption is that mental models are constructed automatically during reading. The minimalists' idea of the theory of mental models is slightly different from what most researchers assume as a standard point of view. The construction of a mental model is an incremental updating of the representation on the basis of the present and past input. So the resultant representation in any given moment guides the interpretation of subsequent input. However, the claim that mental models are built online differs from the claim that mental models are built automatically.
Comprehension proceeds in a linear fashion and is very efficiently organized in real time.
The formation of a mental model is an intentional process, hence not automatic, but it might still occur online. The distinction between automatic and nonautomatic should not be drawn only on the basis of how quickly an inference is generated, as is implicit in the minimalist hypothesis. Because speed alone is used as the criterion for automaticity, the mental-model theory is mischaracterized by the minimalist hypothesis. It is precisely the idea that automaticity and speed are synonymous in the minimalist hypothesis that demands that we know the speed at which we can consider a process as being automatic. It would be very hard to falsify the minimalist hypothesis if we could not specify how fast an inference had to be in order to be considered automatic.