Mathewson's day book, which survives and was reprinted as an appendix in Bill Achtermeier's Rhode Island Arms Makers, says nothing about where he apprenticed who he apprenticed with. In re-reading the entry, Bill concluded he'd apprenticed in Sutton based on some peripheral evidence, none of which is conclusive to my mind. That's the never ending problem with secondary sources. Even in this case where I cannot say Bill was emphatic about it, I clearly didn't remember it exactly as he wrote it.
Welcome was located in Smithfield, RI. At the time, there were only 5 towns in RI and Smithfield covered most of the northern part of the state. It was gradually broken up so I think his home is in what is now Chepachet, RI. A real curiosity is that in The Gun by W.W. Greener, the invention of the choke boring is attributed to Jeremiah Smith, also of Smithfield RI (now Lincoln, RI). I'm very skeptical of that but my best friend in HS lived in the Jeremiah Smith house - which is still there and his sister lives there now.
Bill knew the family and had access to the Mathewson papers, many of which are still in their possession along with Welcome's rifle and fowler, his powder horn and his brother's Dragoon saber. (He was Captain of the only RI Militia Dragoon company in the War of 1812.)
