It gets confusing because most of the town of Douglas (north of the harbour and river) is physically in the parish of Onchan, while that part south of the harbour is in the parish of Braddan.
All of the churches come under the Parish of Braddan.
For census purposes the Town was enumerated as a separate entity (as were Ramsey, Peel and Castletown). However at the top of each page in the census books were places to enter the Civil and Ecclesastical parishes.
As a result you can find, for example, an entry for an address in Douglas listed under the Civil Parish of Onchan and the Ecclesiastical Parish of St Barnabas.
The 'other' two Emmas conisistently give their place of birth as Douglas while the daughter of James is only one to give Onchan and resided in Onchan Parish.
My own experience in using the census material is that the respondents igonred legal points. If they were born in Douglas, they said Douglas. If they were born outside the town they said Braddan or Onchan.