This article presents a unified framework analysis for downlink terahertz (THz)-based multiple-input single-output (MISO) rate-splitting multiple-access (RSMA) systems under spherical stochastic models. To simultaneously achieve the users' full diversity gain, a novel precoding weight design is proposed based on zero-forcing and maximum-ratio transmission approaches. Accordingly, closed-form expressions for the users' outage probability (OP) and throughput are derived in exact, approximate, and asymptotic manners. Additionally, the users' OP minimization problems are formulated and proven to be strictly convex with regard to the common power allocation (PA) factor. To clarify whether RSMA is superior to non-orthogonal multiple access (NOMA) in future THz communication networks, the OP and throughput comparisons have been carried out. Numerical results confirm that: 1) our theoretical analyses exactly match the simulation results; 2) as for OP aspects, RSMA is not fully superior to NOMA in two-user cases, while for multi-users, it only outperforms NOMA in cases where imperfect successive interference cancellation process produces over 10% residual interference; and 3) as for throughput aspects, RSMA achieves the performance superiority over both two- and multi-users scenarios when compared to its counterparts.