Moving an engine back in a front engined sedan is done for two reasons:
1. Increase weight on the rear (drive) wheels.
2. Decrease chassis yaw inertia (MOI).
Number 1 helps with putting power down and must be matched with wider rear tires and changes to spring, anti-roll bar, and shock damping rates. It also reduces forward weight transfer and helps with braking by keeping more weight on the rear wheels.
Number 2 makes transitions (any time the car changes directions) quicker and generally makes the car more responsive.
Both of the changes above, if done correctly, will reduce lap times and make the car more responsive to driver and track input. They also make the car more difficult to drive at the limit and over the limit behavior can be sudden and extreme if the driver is not skilled. This difficulty increases over the course of race as the tires lose grip.
I'm not surprised at all to hear that such radically modified Supras and S14s were actually slower initially. That's to be expected until the car gets sorted and the drivers get better. But there's a huge Catch 22 in getting these cars sorted: Until the drivers get better the car cannot be driven consistently at the limit, lap after lap, to provide data to sort the car. The driver's start to distrust the car and drive slower. Any chassis/suspension changes made using the data from these slow lap times is useless and just works to make the car even slower. The crew chief starts losing his mind, the driver is scared, frustrated, and just wants to go home, and the car owner wonders why he bothers to read anything on the Internet.