So I have recreated the tutorial yesterday and got it working but I had a bit of trouble incorporating it into some other scripts I have running. But in the end I realised that it would limit me a bit too much (the text being aligned to the left and the forced linebreaks - I should have paid attention at the beginning of the video!!).
So all I did was add an object text that would update with the text of the characters at the same place. And with their font set to something invisible I have the animation of the characters speaking and the text is not "flickering" anymore.
Since I am using this in only a handful of short scenes I am soing this "manually" via the editor but I guess if someone was pursuing this further you could script something a bit more elegant.
So in conclusion: thanks for the pointers, this can now be regarded as closed. Just wanted to let you know if anyone ever runs into a similar problem. Unlikely, I know, but maybe someone wants to make an adventure game with ghosts, so it might help...