To achieve an efficient compression and reconstruction of vibrotactile signals in the Tactile Internet, an end-to-end neural vibrotactile codec, PC-NSVC, is proposed. By integrating a residual product quantizer (RPQ) within a deep autoencoder, PC-NSVC effectively reduces coding latency through joint training and inference of the entire framework, while simultaneously enhancing the quality of the reconstructed signals. The RPQ allows for control over transmission bitrates by adjusting quantizer parameters, enabling scalable codec across various network environments and bandwidths. Additionally, PC-NSVC incorporates psychohaptic model to account for the influence of human perception, further improving the perceptual fidelity of the reconstructed signals. A remote vibrotactile sharing prototype, TouchShare, was developed to conduct transmission and material classification tests. Simulation and transmission results demonstrate that the PC-NSVC scheme significantly improves the quality of reconstructed signals at different compression ratios and supports accurate material classification, outperforming existing schemes.