Working on different Tabs of the same website

I need to work on 2 or more different Tabs of the same website. Each Tab with a different log in account. Whenever I try this on my MacBook it automatically changes the Tabs to the same login account, so I end up with just one useful Tab. My PC’s do it without any trouble, so that tells me it’s not the website or the router. How can I fix this in my MacBook?