On an issue, in the people section you can see the watchers:
Screen Shot 2016-11-05 at 16.48.55.png
When you click the counter indicating the number of watchers, you can add watchers as you can see from the screenshot.
Take a note that there is a specific permission that allows you to set who can manage watchers. Without that permission, you will not be able to do this. To set the permission, go to your project settings and find the Permission Scheme applied to your project.
Check/set who can manage watchers:
Screen Shot 2016-11-05 at 16.48.07.png
It is recommended to use project roles for this permission. By assigning users/groups to those roles in your project, you have control over who can manage watchers at project level.
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