the use of patronymics in the IGI has nothing to do with the way the names were recorded by the cleric. The
indexing of the IGI assumes that the surnames in Welsh parishes should be recorded as patronymics until the new style registers started in 1813. So, if you check the register itself, you get for example, 22 January 1810, Martha daughter of Thomas Madock, Trawsduganol ( no surname given for child).The old IGI in batch number C099301 for Llanarthney has this indexed as Martha Thomas and shows her father as Thomas Madock.
https://familysearch.org/ark:/61903/1:1:X1RX-RMQFreeReg also has her indexed as Martha Thomas, father's first name Thomas & the notes say patronymic: father's name is Thomas Madock.
But the new FamilySearch collections
https://familysearch.org/search/collection/listhas her indexed as Martha Madock
https://familysearch.org/ark:/61903/1:1:KCLN-K3WThere's no way for us to know if that family were still using patronymics at that time without checking for more records.
One of the problems with this is you need to know the father's first name to find the baptism unless you search by first name alone which can take a while if it's a common name. Or use the new FamilySearch if the parish you need is on it.
John would not necessarily have become Jones by that time, they might stay John or Johns. I've come families whose surname is David in 1841 & change to Davies by the 1861 census. I've also come across families in parts of Carmarthenshire still using patronymics in the 1830s. In one family one brother stopped around 1835 and the rest of his children were baptised with the same surname as him, but his brother carried on using the patronymic form.