Migrations running on their own causing site down I'm a bit stumped with this one and wonder if anyone else has come across it.

I've a site live which is using the 'Formerly' plugin amongst others, since a recent update the site has gone offline twice in the last week do to the formerly plugin needing to make changes to the database.

I didn't think this could happen on it's own? It's like the plugins migration wants to run on it's own at weird intervals.

Not sure how to debug this, anyone else had this issue?
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.