Most of the cars in the GTR game will have a tendency to understeer--as they do in real life. Push from the diff may only be part of the reason (which could be nearly 'dialled-out' as the diff ramps are adjustable in all the cars.) Being front-engined (ex the S7 Saleen) does not help. (Can't comment about the NGT//GT2 cars)
In most cases, just let the car do the work and don't try and push. Traction is generally excellent on these cars so the car is unlikely to move from understeer to snap oversteer in a millisecond. (unless the tyres are cold!) Wait until the front-end bites and ...............................boot it.
Remember, these cars have a lot of torque so be sure to have lined the car up in a straight line before you give it some.