Non-orthogonal multiple access (NOMA) has potentials to improve the performance of multi-beam satellite systems. The performance optimization in satellite-NOMA systems could be different from that in terrestrial-NOMA systems, e.g., considering distinctive channel models, performance metrics, power constraints, and limited flexibility in resource management. In this paper, we adopt a metric, offered capacity to requested traffic ratio (OCTR), to measure the requested-offered data rate mismatch in multi-beam satellite systems. In the considered system, NOMA is applied to mitigate intra-beam interference while precoding is implemented to reduce inter-beam interference. We jointly optimize power, decoding orders, and terminal-timeslot assignment to improve the max-min fairness of OCTR. The problem is inherently difficult due to the presence of combinatorial and non-convex aspects. We first fix the terminal-timeslot assignment, and develop an optimal fast-convergence algorithmic framework based on Perron-Frobenius theory (PF) for the remaining joint power-allocation and decoding-order optimization problem. Under this framework, we propose a heuristic algorithm for the original problem, which iteratively updates the terminal-timeslot assignment and improves the overall OCTR performance. Numerical results show that the proposed algorithm improves the max-min OCTR by 40.2% over orthogonal multiple access (OMA) in average.