It needs access to all sites because I don't know what would be the Url of your Jira site. You can very well look at the source code to understand what it does with the permission.

However, couple of weeks back I have already announced that I am going to narrow down the permission scope to only access Atlassian sites which would happen in upcoming version about to be released in next couple of weeks. You can look at the announcement in following url and is also shown within the tool's notification section.

https://jiraassistant.com/contact-us/

Additionally, this implementation is already available in Chrome extension. If you want to immediately start using it, then you can try the chrome extension temporarily while I publish updates to other browsers.