What do 0s in stageR mean?
In stageR, we automatically return stage-wise adjusted p-values of zero for transcripts coming from genes that were found to be significant and only have 1 transcript, when testing for differential transcript expression (DTE).
Similarly, when testing for differential transcript usage (DTU), we return p-values of zero for transcripts derived from a significant gene consisting of no more than two transcripts (based on the tx2gene object you provide).

Transcript-level p-values for non-significant genes should not occur. We provide NA's for genes with only one transcript for DTU, and by default you should get NA p-values for non-significant genes, since these genes do not proceed further than the screening stage.

Could you provide some more details on the analysis? Which multiple testing correction have you selected?

Would it be possible to provide a reproducible example for your analysis?