I would like to add to this that when I change the "Start Orion With" setting from "All Tabs from Last Session" to "New Tab" then it starts to work properly (meaning that it opens the link from another app even when Orion had not been loaded into the memory previously).
Thus, this definitely has something to do with how Orion restores previous session, it probably "forgets" the page that the user was going to open from another app after restoring its previously saved tabs.