How much difference is there.
By'starts before' do you mean milliseconds or two measures?

It should be easy enough to fix between the settings on the two machines.
One may have a smaller buffer (latency) or it may be a matter of inserting/cutting space on certain tracks.. but you could likely learn to line them up, and probably get a routine figured out, if these files go back and forth. Sometimes usiing MIDI tracks can reduce the time to get the job done compared to:

sender: convert to audio
sender: upload (larger file because it's all audio)
receiver: download on the other end (larger file because it's all audio)
.. and then you are stuck with the MIDI renderings to audio (may be a good thing, may not). I like to have the MIDI data for later just in case.

If it's fixable by highliting the one track, then holding control to select all the tracks you want to change, then insert/cut the space needed .. that may be faster once the parameters are known. If the files are going back and forth a bunch of times, I've found this to be more efficient sometimes for both parties.

Oh, and make sure you are using the same synth for MIDI .. that alone can change things.

I do not work here, but the benefits are still awesome
Make your sound your own!