Your observation is wrong. There is no such thing. The behavior is not expected and not unexpected, it is what you choose.

This is not about buttons. And it is not related to your Web page/application.

This is just the Download option you have to set up for each profile on a browser. You set it the way you want for your Chrome profile and haven't done that in Firefox, that's all.

Please adjust the Download option to your liking where you need it. Then you will see the proper browser behavior.