I cannot find any trace of this marriage in the civil marriage indexes either, anywhere in Ireland. Not in 1893, nor in any year near it. If the couple had other children born in Scotland, I’d be inclined to get those certificates to see if different information is shown. Though the information on this certificate is evidently fully legible, bear in mind that the Registrar had no way of verifying it. He/she simply recorded what the informant said. Sometimes people made mistakes or had their own private reasons for giving inaccurate information.
If you think it was an RC ceremony, you could write to the parish priest and ask him to check the church record to see if it is there. (It was not unknown for the record of a church wedding not to be copied to the civil registrar, and so be missing from the statutory records).
Having said that there are a lot of Presbyterian and Church of Ireland McMullan & McMillan families in the Portrush area. Only a handful of Patons in Co Antrim in the 1901 census. All Presbyterian or Congregationalist (a sort of stand alone Presbyterianism). I’d keep an open mind on the denomination. Tradition was to marry in the bride’s church, so that may not be the same as that subsequently attended by the family.