As Tournicoti stated, adjusting things like restitution can help. The strength of the impulse applied will be proportional to the input velocity, which for kinematics is proportional to the delta between the current and target pose divided by time-step. If you have a very small time-step or move the kinematic by a large amount, the input velocity could be very large. Additionally, a large amount of motion may cause significant penetration between the shapes.
Which version of PhysX are you currently using? Are you familiar with contact modification? Contact modification allows you to modify a number of contact properties prior to the solver being run, including a per-contact field called maxImpulse. This can be used to restrict the magnitude of the impulse that the solver can apply for a given contact. In earlier versions of PhysX, e.g. 3.0, 3.1 and 3.2, this was only partially supported so it only allowed you to make the SDK ignore contacts by setting the maxImpulse to 0; any other value did not affect the response. As of PhysX 3.3, this modification is fully-functional for discrete simulation. This may be useful to you if you can’t find a way to tune your simulation to reduce the input velocity from the kinematics.