When the aircraft is in motion, iFly typically adjusts the ownship location on the moving map so that you can see more of what's in front of you. So, if your map is oriented to "Track Up", your ownship icon will settle around 1/3 of the way up from the bottom of the screen, leaving 2/3 of the screen in front of your plane. (If your map is oriented "North Up", then your ownship will move around on the display to try to keep ~2/3 of the display in front of your plane.)
When you are not in motion the ownship icon will return to the center of the map.
This behavior can be turned off (so that your ownship stays centered on the map) if you prefer. Menu > Setup > Map Settings > Auto-Track Plane, then select "Center Aircraft (no skew)". (The other options on that menu affect whether the map will automatically time out and pan back to track your aircraft if you pan (drag) the map away from your plane.)
You don't specify whether you were in motion or not when you observed your behavior. Even if you were motionless, it's possible that when iFly connected to the Stratux, it got a slightly different GPS fix from the Stratux than what it had from the 740's internal GPS and so it thought that it was moving.
After that, if the Stratux had a solid GPS fix, then after a short time you should have seen the ownship settle back to the middle of the map. But if the GPS fix was "noisy", then iFly might have continued to think you were in motion, and you might have seen the map jumping around somewhat erratically.