Kyle, if you still remember the bug on my xiaomi redmi 2, I have tried it on another phone and I guess I know the real cause (yeah, even the custom ROM method still encounters this bug).
I don't know why, the cut at the beginning of the song is still there with the custom ROM, both on my redmi 2 and another phone (this phone uses Google official ROM though, it's an android one phone). But, with custom ROM and Google ROM, the cut is just too little to notice, but still there, while with MIUI ROM, the cut was almost a second and noticeable.
So, I tried to check sound setting, and something weird going on there.
If I chose to enable "Touch Sound", the bug would not appear unless I chose to turn down the ringtone volume (not muting it, but moving the slider all the way to zero). And If I chose to disable "Touch Sound", no matter how big or small my ringtone volume, the bug will appear again.
And almost forgot, the bug happened if I played a song from speaker > paused it > rewind it to the beginning > and play it again but with headset.
It also happened to any other media that uses speaker. in my case, I played a YouTube video from speaker, and then came back to Gone Mad to start a song but with headset on, and that bug appeared again.
I was still unsure if it that only happened with GoneMad. So I tried Google Play Music and some other players. They didn't exhibit the same bug.
If I remember and am not mistaken, the bug wasn't there in earlier version (But I guess I need to check again, trying to find the apk on my old backup archive). So, perhaps you could give me some... insight on what really happened?