I hope you take what I'm saying as constructive, I am not here solely to be a Debbie Downer, though I understand what I'm saying may sound harsh. I went back to watch a few more times and be very specific about what I think is wrong and suggestions.
Correct, but your transition to it from :18 to :21 is, as well as some bleed-through around :24 that comes in with the dialogue "Hey!". The audio transitions are somewhat empty sounding, by which I mean it dips quiet in the middle of the transition as if my whole viewing device's volume were briefly turned down and then back up. This happens in the middle of a shot, which to me feels like an unmotivated change in music, like one song stopped and another song started. The actual music while the ship is swallowed was originally the end of a longer piece of score, but with your transition it is now also the beginning of the piece. If you blend the transition at a location more motivated by something visual, you can probably make it feel like it's a more like a natural extension of score rather than a stop and a start. Cutting a few frames to a few seconds somewhere to match up the timing on the two musical "beats" may be necessary. I'm not in your editing timeline, I don't know specifically what will work in your use case.
I'm not commenting on the differences in look between the sources. I mean the camera motion and info conveyed in those shots don't feel like they line up. The guys in the Star Wars shot are running to something, and the walls they run past have no doors. The way we follow them for two shots, it seems like next we're supposed to see what they've run to. But instead we see similar but different guys in a similar but different place. It's temporally and geographically confusing in a split second as it happens. I understand afterward they're supposed to be or represent the guys running outside the door, but for a first time viewer, that may be too late. This is the intro so it's also the first impression of the edit.
I was specifically talking about that first transition to Rogue One footage, the same one where the guy is yelling but we're just hearing it fade in. That same footage has a shake to it, but we hear no rumble and the alarms stopped, even though it's supposed to be the same place as what we just saw and heard with R2 and 3PO. In the shot with the droids, the footage has a shake to it, because the ship has been hit, which we hear. Adding a rumble sound will help cover the audio transition.
Again, sorry. I know I sound harsh. But try to remove yourself from it emotionally and put yourself in the shoes of someone who is not watching a fan edit of SW and RO but is watching this as its own movie with no prior knowledge of either source.