I have the JIRA Cloud Slack app successfully connecting a Slack channel to a JIRA project. When comments are posted on a ticket a notification is posted in the channel by the Jira Cloud bot.
Additionally, I have connected my Slack account and JIRA account. When I comment on a ticket and mention myself, the Slack notification has a Slack user tag for the comment poster, but not for the user mentioned.
E.g.
@nick (tagged) commented on a Story in ToDo
XX-1 Test story
"@nick (not tagged) please update this ticket."