If the sequences are 20-something bp long then it appears logical to me to throw away any reads that are longer than that after adapter trimming, at least if you want to quantify the mature sequences. That would at least remove the obvious noise. For salmon how did you index the the transcriptome? You would need to lower the default kmer size of 31 quite a bit to even be able to ma these small sequences. And if so I think you would need to use the genome as decoy to have a notable advantage of salmon. You would actually not need tximport as small RNAs do not have isoforms, do they? Can you add some details? By the way, is this normal RNA-seq or specifically a smallRNA-seq, if the former then these small RNAs will not be properly represented, both because standard RNA extraction kits do not capture them well and because the size selection steps during library prep are optimized for fragments notable longer than 20-something bp (rather in the 200bp range).

You may well get lots of protein coding genes, depending on what's in the transcripts file. Do note that most miRNA transcripts are complementary to some portion of the mature mRNA of their targets, which is how they work after all, so it's not unexpected that salmon would count reads complementary to a transcript as a hit. There may be some way to tell salmon not to do that, but I would in general not use salmon, instead I would probably use bowtie. You absolutely don't want gapped alignments, and you don't want the aligner to think that you have paired end reads (you don't, do you? That would be hilarious) because one of the pairs will be on the opposite strand. You could look at the documentation for GeneGlobe to see if they say how they do the alignment, but I am pretty sure they just use bowtie.