Hi Tim, welcome to the OpsGenie forums!
I’m honestly not sure about the solution here, but we can brainstorm together! I believe in JIRA SD, there is a rule configuration which defines when JIRA should be sending data towards OpsGenie. I think there, you can capture the logic - to only send data towards OpsGenie if the priority equals a certain value, or if the priority changed
Once you got that, our integration should be able to pick it up and create the alert properly by our default rules, and if not, we can work together on the Advanced Settings to react on the new mechanism. The important point is to grab data from SD when the desired changes happen on the ticket!
Can you give this a try?
You may check this document for information about the Custom Rule in JIRA: https://docs.opsgenie.com/docs/jiraservicedesk-integration
As for the second question:
I’m afraid adding a tag to the alert upon an action in JIRA is not available by default. The only solution would be a custom script hosted somewhere in the middle. This script should listen to the changes in JIRA, and execute the Add Tag request in OpsGenie towards the existing alert. Far from a straightforward solution, but certainly possible. What tag would you like to add after which changes in JIRA?