Well it depends. I would say if he wants to celebrate with her then maybe. Some men have certain traditions that they do. If you knew about it before then there’s no need to change them. That doesn’t mean that you can’t take your man on a nice bday date or activity separate from his mom.
Now if that’s not the case then you don’t always have to plan a birthday celebration to include his mom. You could make your plans and then if she wanted to do something special with her son she can. This will work regardless if you two get along or not.
I hope that helps. Don’t feel obligated to include his mom in your celebration of his birthday. He’s a big boy now.