Non-Coherent Rate-Splitting (NCRS) was recently proposed as a practical multiuser coding and decoding scheme to increase the spectral efficiency of multibeam satellite communication systems. In this paper, we further study the practical realization of NCRS. We propose a modified coding scheme (NCRS) that is robust to a nonzero time offset among beams. In NCRS, as opposed to NCRS, the beams send independently channel encoded and modulated waveforms. We assess the performance of NCRS* in terms of the achievable rate region. It is shown that NCRS* performs worse than NCRS, but better than or comparable to other competing schemes, which, as opposed to NCRS, require flexible bandwidth allocation or perfect synchronization at the transmitter. We also propose a new N-MAP algorithm for the practical implementation of NCRS receivers. Similar to the existing UMAP algorithm, N-MAP takes into account the modulation used by, and the time offset between, the signals received from the different beams. In most cases, however, N-MAP has a significantly lower complexity than U-MAP.