What percentage of RNA splicing happens during transcription?
I don't think it will be possible to give a conclusive answer to this question, because a) it's a matter of active research and b) the rate / percentage of transcripts that are fully spliced co-transcriptionaly is almost certainly not constant but will depend on a lot of factors &amp; regulatory mechanisms.  

Another important detail is that this analysis / paper is based on mRNA sequencing, which uses oligo-dT primers to enrich for polyadenylated mRNA molecules. However, oligo-dT primers can also bind to stretches of A's inside of RNA molecules (this process is called internal priming) and since such stretches are more common in introns compared to exons this may contribute to the abundance of intronic reads in mRNA sequencing data (I don't have a good literature source for this specific case, but it's a known 'issue' for sure).

Maybe some of these reviews are also helpful (not sure if all are freely available):


Splicing and transcription rates in living cells
Environmental influences on RNA processing  
Co-transcriptional spliceosome assembly and function