The behavior you saw should be expected. I-optimal or D-optimal are OPTIMAL for the number of runs you picked. By building a more complex model to force interior points with the same number of runs will have to increase the prediction variance.
There are several points here to keep in mind. I will discuss first by ignoring the process factor as I think there may be some confusion about the mixture model.
Mixture models are very different from the standard regression models. As Lou indicated, a 2-way interaction in a Scheffe mixture model (which is what JMP is fitting) is equivalent to a squared term for a continuous term). However, the two-way interactions in a Scheffe model are only looking at a curvature effect along the axis between the two components that are in that interaction term. For your three component case, that would be curvature along the edge of the design space.
So given that, the I-optimal or D-optimal designs will choose the best design to estimate your model. If you are only trying to estimate curvature along the edges of the design space, there is no need to put points in the interior of the design. Anything on the interior will do little to help you understand what is happening at the edges of the design space. Think of just a single continuous X. If you only specify a straight-line model, you only need experiments at the ends of the range. You need to specify a quadratic to force a third level.
The model that is needed to start putting points in the interior of a mixture design space is to add 3-way interactions. These are called cubic terms (actually, special cubic terms) in the Scheffe mixture models. They estimate curvature between 3 components at a time. Since you have a three-component mixture that will force at least one point into the interior of your design space. The I-optimal design will tend to put more points in the interior of the design space in order to better estimate that three-way term.
Adding the process factor does not change things too much to what I typed. However, that model gets more complex and there may be some things you want to do to ensure you are getting at least three levels for that process variable.
Dan Obermiller