What's your team's best practice when using JIRA (on premises or cloud) and VSTS or GitHub?

Who manages issues/tickets and are they duplicated in both locations? Is one for PM only and other for Devs??

We have both tools and I'm trying to figure out a workflow that doesn't kill devs and PMs.

We have Office 365 so I heavily use MS Flow to help (Jira bug turns into vsts work item) etc, but any insight from anyone who has a similar setup would be appreciated!