First of all, thank you very much for trying to help. I don't use Cubase, I use DP, and after a lot of experimenting I found a solution, but I still don't understand why the original file does not work. The problem finally is not with the Synchro strings (phew!) but in the file. But I still have no idea what it is.
Here is what I did: I copied the problem track into a new track and sent that to the Synchro strings. Now all behaves normally. Same midi data exactly, different behaviour. I can see no difference at all in the 2 event lists so I have no idea why the first track does not work (and it still does not work if I go back to it) and the new copy does.
I tried saving the piece as a midi file, and importing it, and all is fine.
In all these years of working with DP and virtual instruments I have never seen this before!
Anyway, at least I can work properly now in the (copied) file.
Thanks again!