I recently played through the main quest again and remember Mankar only talking about the invasion of Tamriel, not all of Nirn. I know that's not really evidence that Akavir wasn't involved, but certainly it seems like the Mythic Dawn operated only in Tamriel. Since the Mythic Dawn agents were the ones actively opening the gates early on in the crises, I'd guess there were none opening on Akavir at that point. Once the barriers were down and Dagon could punch through to the Imperial City on his own without needing gates opened from the Mundus side, then it's plausible to assume that gates could have also opened at that point into Akavir. They wouldn't have lasted long however as Martin did his dragon dance pretty quickly after that. It's of course possible that Dagon also had other agents working in Akavir as well, doing what the Mythic Dawn were doing in Tamriel. My guess however is that the invasion was only focused on Tamriel. If his plan worked, and Tamriel was conquered, then he could move on to other regions of Nirn at his leisure.