Hello,
This is an interesting question. I'll attempt to clarify some based on my reading of the STAR manual, however I'm also going to pass this question to some of my peers for possible clarification.
In general, for most of the lab work that we have done, Single-Pass mapping is performed, so for the experience closest to that we are expecting, I would recommend that you use single-pass in your runs.
However conceptually, whether we use STAR in single pass or two pass mode, it will provide us with aligned reads, split over certain positions. ex: found one read which matches half to the location of exon1, and the other half to some intronic location. Or maybe the read is split over three or more locations, etc. The idea being, the end result of STAR is still not any kind of quantified result, but just aligned read-pieces.
This still holds true in two-pass mode. However, by using a lower stringency for the second pass, and also allowing some of the de-novo exons detected by the first pass to be considered "annotated", there will be fewer unmapped read positions, and thus there is potential for more odd splicing patterns to be captured. See this related figure from here, which I believe details a similar approach to STAR:
https://academic.oup.com/bioinformatics/article/32/1/43/1744001
Having more unique mapped reads will help majiq's accuracy when some of these novel alignments may be thrown out by the single pass version.