This is a working solution to add JIRA Watcher with a ScriptRunner Listener

AddJiraWatcherListener.groovy

//put this in <jira-home>/AddJiraWatcherListener.groovy and activate through custom listener
Import com.atlassian.jira.event.issue.AbstractIssueEventListener
import com.atlassian.jira.event.issue.IssueEvent
import com.atlassian.jira.ComponentManager
import com.atlassian.jira.issue.Issue

class AddJiraWatcherListener extends AbstractIssueEventListener {

    @Override
    void workflowEvent(IssueEvent event) {

        def componentManager = ComponentManager.getInstance()
        def watcherManager = componentManager.getWatcherManager()
        def userManager = componentManager.getUserUtil()

        def watchUsers = {usernames ->
                usernames.each {
                        def user = userManager.getUser(it)
                        watcherManager.startWatching(user, event.issue.getGenericValue())
                }
        }

        def users = ["skler", "username2", "username3"]
        watchUsers(users)

        //log.debug "Event: ${event.getEventTypeId()} fired for ${event.issue} and caught by ExampleListener"
    }
}