Vlad I actually was able to recreate this issue. I did try putting both sites on compatibility mode as suggested and the problem still exists.
It appears to be caused by the JavaScript on an inactive tab changing the focus of the currently active tab, which could potentially be a security issue.
I created a JSFiddle to exhibit the problem here. If you open the JSFiddle in one tab, click the button labeled "This will steal the focus of any Orion tab in 5 seconds" and then select an input field on a different tab, at the end of the JavaScript timeout (5 seconds in the demo), the inactive JSFiddle tab will steal the focus back to its input field using the Javascript focus()
method as shown in this video:
Safari does not behave in this manner, its focus stays on the active tab only.