All exports should be exactly as they are in the sequence. The only reason I can think of for this type of error is something wrong with the playback of the exported file.
I have just exported it at 1/4 of the real resolution, to try and eliminate any stress on the video card, but the problem is still there (and the same delay).
It is uploaded here (only 5mb, if you don't mind having a look):
A picture of the waveform in AE is here. As you can see (that is the start of the 'scene'), it is perfectly aligned to the transient.
The cuts seem to be very well timed with the music for me. This supports the idea that there's something wrong with the playback of the file on your computer.
Here's a hint: Don't use Qcuiktime - for anything. Don't use them as raw media, don't export them as files, don't use the player. Just don't even install Quicktime on your machine. Life is good that way.
I wish I didn't have to use Quicktime, but its for a uni assignment.. and our lecturer seems to think that anything not Mac is terrible.. and so we have to hand in the files as .mov's. I agree that Quicktime is terrible.
I tried it in VLC player, slight delay but not as much. Tried it in Windows Media Player and there's almost no delay. I'll just have to ask that its played in Windows Media Player then. Thanks for your help.