Ok, I located the source of the problem – I had to time stretch the layer with the pasted mapped data from Mocha.
The face didn’t follow the actor fast enough (it was lagging behind), so I changed the ‘stretch’ parameter from 100% to around 40% and it matched the movement appropriately.
Although, I don’t have the idea why I had to change the stretch – the tutorial didn’t mention it. Could the fps be the source of this? (the movies both have 25 fps, but the mapping in Mocha was done in 10fps)