If your child is really upset in a contact session the person they are spending time with will be expected to be able to meet their needs and if needed they will be supported to calm your child. These are important skills that will be required if or when the service moves out of the centre. It is also important that your child builds a relationship and trust with the person they are spending time with so that this can be the initial stepping-stone towards allowing this parent to meet their needs.
However, there are some, very rare, occasions when children cannot be calmed, and this is neither the fault of the child or the person they are visiting at the centre. In this scenario it is possible that sessions will be bought to an end early. Child contact centres are there to ensure the safety of children, which includes their emotional wellbeing. Centres will not allow children to become traumatised or to develop and or maintain negative memories or associations with the centre because this might stand in the way of future progress.
Initially, the centre might invite you to remain present in the centre. Possibly within a waiting room so that you can be there for your child if they become unsettled. Moving forward they will probably encourage you to be leaving the centre during contact, they will be able to call you to come back if you are needed.