I don't agree that it's absolutely nothing to do with your employer, because I have had employers where some relationships were prohibited, (e.g. different levels in the same reporting line,) and I would at least have to report this relationship (being an ex) to my current employer. However, your employer is aware.
How much do you actually have to work with him? Do you need to speak to him, hand over work to him or receive work from him? I am assuming that if there's a canteen and shifts, it's not a tiny workplace.
It might be that there is little practical option over his shifts - I am involved in organising rotas at work, and if we have people off sick or on leave, there's very little room for flexibility. Also, if he's been there about a year and no problems have come up, such as you openly disagreeing with each other in the workplace, they're probably thinking it isn't a problem any more.
Make it not a problem. Don't worry about when he's on shift - just do your job. Say nothing to him other than what is required for the job. We all have to work with people we don't like at points in our careers - just be adult, polite and professional, nothing more, nothing less. If he taunts you or anything, then you can go to HR for harassment- in which case it will be important to be able to show you haven't put a step wrong, not wound him up in return. He might have applied just to rile you - don't let him. He's not worth the headspace. If he did join to annoy you, rising above it and behaving serenely as if you don't care will probably be the best way to get back at him.
If you want to stay, you need to find acceptance of the situation- otherwise, your only option will be to leave.
Do go for CMS (you know he's earning.)