When I was a sim instructor and building time, I logged the 100 hours that can be put towards your ATP credit in a separate logbook, I logged all the time during my type training and all time I was a seat fill. The training center where the sim is should be able to give you a printout out with times in the sim and instructor giving instruction abs the lesson syllabus reference to the purpose of the lesson. You can use that as your log.

I never counted this as anything other than sim time. Logging it as dual is silly as all sim time is instruction.

I also had a copy of the simulators FAA registration, and the training centers credentials.

I wound up with over 1000 hours of logged sim time, but only 100 meant anything.

That being said, I have never had one issue in airline training, purely due to my comfort with the sim world.