Common assumptions in most of the previous nonlinear networked leader-follower systems are that the leader is provided as a constant signal and that the controllers are designed for either the joint-space regulation or the translational Cartesian-space motion control. This article addresses the control issue of the delay-induced horizontal shift effect when the leader is moving with a changing speed. A novel mixed-type feedback is introduced to reduce the horizontal shift effect so as to minimize tracking errors experienced by the follower agents. In this article, we also study the complete pose control using a nonsingular terminal sliding mode (NTSM) method. A stability analysis is provided to prove the finite-time boundedness of the tracking error signals. Quantitative evaluations of the multiple effects on the error bound are conducted to facilitate the subsequent control design to improve the performance. Numerical simulation results of a team of two degree-of-freedoms (DOFs) manipulators demonstrate the improved tracking performance of the end effectors with small bounded errors which are affected by network delays, maximum assigned accelerations, and the selection of control gains. The experimental results are provided to demonstrate the performance of the developed controller.