I used to design the mechanical side of the kinds of simulators you’re talking about. Most likely, what they’re using is a generic simulator, probably PC-based albeit running custom software. I’d expect a mockup, generic cockpit with some generic flight control hardware (either high-end commercial units, or older/spare units taken from a FBW military aircraft).
I’d bet they were being used fairly early in the dev cycle—as soon as you had a preliminary concept and could generate some performance characteristics, you could start mocking up a simulated vehicle to test it. I know on the programs I worked (transport-category civil aircraft) we were using custom-written sim software for the aircraft behavior side, a commercial PC sim for the out-the-window display (our custom sim just fed it a position), and supplier prototype/eval flight control units for the pilot controls. We used it very early on to try out some cockpit interaction ideas, flight control laws, etc.
This was probably two years before we started building the iron bird and avionics test rigs (which also ran hooked up to simulations, but with the aircraft side being real hardware—avionics, flight control electronics, etc). Our test pilots spent a lot of time in them but it wasn’t really “learning to fly” the airplane, more practicing procedures and rehearsing tests. The moving-base pilot training sims didn’t really come online until after the flight test program was well underway.
We also had an avanced-concept really early prototype sim that was all PC-based commercial sims and hardware running in a wooden mockup; we used that for a few theories we had on synthetic vision and other advanced avionics concepts.
