Mum and dad will have a meeting with the centre before the first session. The centre will ask them not to talk about things that might make you feel uncomfortable. If they do this in supervised contact the staff will hear and ask them to stop. Otherwise, you can always tell the person you are in contact with that you do not want to talk about that. The staff will always support you.
In supported contact, the staff might not hear the person you are having contact with, saying things that make you feel uncomfortable. So, you might need to help them out by letting them know. If you don’t want to do this, you could always tell the person you live with so that they can work with the centre or the person you’re having contact with to make sure this doesn’t happen again.