If I understand your concerns here, you are looking to understand how much time is expected to take between a commit in github and when that commit shows in Jira.
The DVCS integration in Jira works in two ways:
So while method #2 can make this info appear nearly instantly, there are sometimes conditions that occur that prevent this from working. In which case, Jira could be only updating with that info once every hour. If you're seeing an unexpected delay of this info then I would recommend taking a closer look at this knowledge base article, Delays for commits to display in Development Panel in Jira server. It does provide a more in-depth explanation for this behavior and some work-around steps you can follow to correct this.
I hope this helps, please let me know if you run into any problems with this.
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