"Basically, you have to code each "task" in the RTOS such that they will terminate in a finite time."
This is actually correct. The RTOS will have a system tick defined by the architecture, say 10 millisec., with all tasks (threads) both designed and measured to complete within specific times. For example in processing real time audio data, where the audio sample rate is 48kHz, there is a known amount of time (in milliseconds) at which the prebuffer will become empty for any downstream task which is processing the data. Therefore using the RTOS requires correct sizing of the buffers, estimating and measuring how long this takes, and measuring the latencies between all software layers in the system. Then the deadlines can be met. Otherwise the applications will miss the deadlines. This requires analysis of the worst-case data processing throughout the entire stack, and once the worst-case is known, the system can be designed for, say, 95% processing time with 5% idle time (this processing may not ever occur in any real usage, because worst-case data processing may not be an allowed state within all layers at any single moment in time).
Example timing diagrams for the design of a real time operating system network app are in this article at EE Times, PRODUCT HOW-TO: Improving real-time voice quality in a VoIP-based telephony designhttp://www.eetimes.com/design/embedded/4007619/PRODUCT-HOW-TO-Improving-real-time-voice-quality-in-a-VoIP-based-telephony-design