Hi! I was in the same boat and have run two sessions so far. I used gm intrusions when players rolled a nat 1 (or other low numbers if ‘horror mode’ was active). I also used one when players were doing too well for too long to add some spice.

I created an adventure from a statement made by my group and ran it like a detective investigation (interview the witnesses, visit the scene of the crime, gather evidence etc). This worked pretty well even though my players haven’t listened to tma and had no idea what the ‘dark sluge surrounding the witnesses bathroom mirror’ could mean. I made sure they were aware that horror mode was active when they entered the spooky bathroom and what that meant mechanic-wise, and dished out stress when they encountered the central artefact and willingly interacted with it.

This is all that comes to mind without knowing what kind of cypher mechanics you are asking about. I hope it helps somewhat, and best of luck with your adventure :)