John starts appearing in records in 1662, when he, "of Providence,"" sold part of his town grant to William Carpenter. He may have settled in Providence as soon as the family came to Rhode Island. I haven't found proof of his wife Elizabeth being the mother of his children.      

children of John Smith (the Mason, Jr.):

Leonard b. abt. 1640 (land laid out at Prov. in 1662)
John
Benjamin
Eleanor
Joseph
Mary

vital records sources:

1.