All the options fields are stored in browser local storage. so I think it will not create an issue in production where most of the users stick to one company with their browser.

however, you want to solve the issue you can extend the javascript part and add the addition keypart as compnay_id in the local storage identifier. 

https://github.com/odoo/odoo/blob/13.0/addons/web/static/src/js/views/basic/basic_controller.js#L462
you can get allowed_companies and current_company from the session.

​