The impact of successive interference cancellation (SIC) in non-orthogonal multiple access integrated sensing and communications (NOMA-ISAC) is analyzed. A two-stage SIC-based framework is proposed to deal with the inter-communication user and inter-functionality interferences. The performance of sensing and communications (S\&C) is analyzed for two SIC orders, i.e., the communications-centric SIC and the sensing-centric SIC. For each design, diversity orders, high signal-to-noise ratio (SNR) slopes, and high-SNR power offsets of the sensing rate (SR) and communication rate (CR) are derived as insights. Analytical results indicate that i) the main influence of SIC order on the SR and CR lies in the high-SNR power offsets; ii) ISAC provides more degrees of freedom than frequency-division S\&C (FDSAC). Numerical results show that the SR-CR region of ISAC entirely covers that of FDSAC.