I'm using DEXSeq for the analysis of 16 human tissues. I'm trying to identify exons that are differentially expressed in one tissue against all other tissues and eventually trying to identify exon skipping events between tissues. I ran the whole pipeline of DEXSeq on all the sample for all tissues. What I understand is when I have exon with differential usage in the results table, that means it is differentially expressed in at least one tissue but I can't determine which one. I also can't determine if it is differentially expressed on more than one tissue, is that right? is there anyway to know such information?
My guess is the tissue with the largest exon usage coefficient is the one that is differentially expressed but the question is: it is differentially expressed against all other tissues or again only one of them? how can I know through the numbers? I examined the intermediate results for the dxd object but what I found are columns for all the samples versus sample 1 only. What does that mean? What I'm trying to know is if one exon is differentially expressed, in what tissue? and against what tissue? Can you please help

Yes, the LFC is always given relative to the first tissue, as is usually done in linear models. If you want to see the LFC between the, say, the second and the third tissue, you can simply look at the difference between their respective coefficients, because the effect of the first tissue will then cancel out.

"My guess is the tissue with the largest exon usage coefficient is the one that is differentially expressed but the question is: it is differentially expressed against all other tissues or again only one of them?" -- It could also be differentially expressed against two or three of them. This is not a yes/no (or one-vs-all) question, and this is why there is no easy answer.

If you need a stastistically rigorous answer to the question whether exon usage differs between two specific tissues, you could rerun DEXSeq with only these two tissues.

A simple way might be to subtract from all coefficients the mean over all the tissues, to get the tissue's deviation from average, and inspect this, maybe visualized as a heatmap, to see which tissues are similar and which differ.