I just downloaded the stems and pulled the drum track into Melodyne, it comes up at an average of 118.931, so set up a new project in X3 as 118.93 and imported the 8 stems (from the \BeatportRemixPackage-TearsForFears-PaleShelter\TearsForFears-PaleShelter-BeatportRemixStems folder).
I am not familiar with the song, so I muted the 2 synth and percussion track and jumped out to ~ bar 12 and it seems pretty synched. I didn't delve into it much beyond that though.
It seems this remix contest is rather skewed, as it has stems (and a cfg) file in that download specifically for Ableton. I would recommend the stems from the directory above, as the others seem to be specifically linked to that config file (i.e. require Ableton).
Edit: I just listened to the actual original song, so your timing issues may be that those initial bars are, in fact, added to the song. Not sure, but the "official video" starts ~2 seconds before that initial drum beat. They have a nice propaganda tag on the front of that vocal track (backwards lyrics)... says "The sickness in the system is an amplification of the sickness in the individual"
Edit2: Those 8 stems seem to be synched to each other pretty much, but do need to be slid some. By leaving a lead in on the song, they can be synched where the first couple bars of the drums come in and are close. They seem to stay well synched, but the timing does drift, so if you are looking to insert MIDI, you may need to audio snap from that point.