Migrations running on their own causing site down
Plugin Migrations run as soon as Yii finds a new file. So as soon as there is a new file in your migration folder Craft starts to migrate it the next time someone triggers Craft tasks (usually by entering the CP). When you hit the Update button in your CP there could be that chance that a plugin makes an update -> pulls those migration files. 

What do you mean with "how to debug this"?

If you want to remove the task, you can clear the task table and get rid of it. You can take a look at the plugins migration folder and see if there are any new files.