I'm not sure about RSEM but STAR is deterministic. Here is an answer from Alex (developer of star) from the past. If I recall, RSEM is a transcript identifier, if you haven't upgraded STAR recently, I'd look into --quantMode in STAR, it'll save you time, and is an in program identifier.
Looks like OP saw it but for future people going to this thread, here is developer of STAR's answer:
STAR alignments are always deterministic, however, the order in which they are output, as well some flags/attrbiutes (primary flag, HI) are not always deterministic.
With default parameters, and running on one thread, STAR is fully deterministic, down to the order of output alignments.
With multiple threads, the order of the reads in the output is not deterministic, as STAR reads/maps/writes reads in chunks.
However, the alignments for each read are completely deterministic.
With --outMultimapperOrder Random, the order of alignments for each read is no longer deterministics, which also affects primary flag and HI attribute.