I think for the early ones (Readme, LSD, LCD, SNDS, B.I.G.) it was mostly C-64 compositions. So as far I know, those songs needed no composition tool. Although the note-player needed to be remade for the ST and sound programming done from scratch as well.
For newer original compositions (like Thalion games, TCB and Lost Boys demos..) I've had a glimpse at a tool called TFMXMMTEX-Editor. It is tracker-like, but not that easy to use, at least not without a manual.
And to answer the obvious follow-up question; sorry no I don't have a download-link for the program.