I’ve found over the years that differing frame rates of source material is almost always going to cause headaches. I’ve used Premiere Pro since long before it became Premiere Pro, used Media 100 back in the day, occasionally use FCPX and Avid, and all of them have difficulty with differing frame rates on the timeline. Just expecting an application to handle different frame rates as if they’re all the same (one second is one second, no matter how it’s split up) isn’t realistic. Progressive-frame video on computers (and iPads/iPhones) isn’t handled in seconds, it’s handled in frames.
Smart phones aren’t always exactly consistent in the frame-rate at which they capture video, and other devices vary, as well. There’s also something called drop-frame and non-drop-frame, which is why some devices that purport to be shooting at 30 FPS actually record at 29.97 FPS, or rather than 24 FPS actually records the footage at 23.976. For the most part, and particularly on short movies, having slightly different frame rates on a timeline won’t have much impact on your work, but sometimes after a bit, there is a synchronization slip, as the original poster stated.
Premiere Pro and AfterEffects give you the option to “interpret” the footage — that is to impose a specified frame rate on the footage. (Other pro desktop apps offer the same feature, often called by other names.) So, if your device captured at 29.97, but your timeline is 30, you can interpret the footage to be 30. The software speeds the footage up by a little less than 1%, which is imperceptible to just about every human on the planet, and it allows 29.97 footage to stay locked in sync with 30. iOS handles video a little differently than MacOS or Windows, so “interpreting footage” may not be possible.
The best solution is to ensure that you’re capturing all your source material at the same frame rate. Obviously, sometimes you can’t control the exact frame rate, and when that happens, you just have to jump through a few hoops to make things line up, whether your using LumaFusion or Premiere Pro or FCPX; it’s just a property of how media files work.