Here is an old post from November 13 2009. I reprint it because the attached thread establishes that S Joseph is not part of the Canon in the 1962 Editio Typica. Accordingly, his insertion in Masses said by virtue of Summorum Pontificum is apparently illegal.
Readers also discuss the important fact that, pretty universally, the rather unsatisfactory rite of "1962" is not celebrated as printed but with a lot of the manners, mannerisms, of the previous dispensation. These variations presumably now (Canon 26) have the prescription of consuetudo; and remember O'Connell's discussion of consuetudines contra vel praeter legem.
This is what I wrote in 2009: A very strange youtube video has appeared, from the Ecclesia Dei Commission, showing How To Say Mass. I mention here only the oddity that S Joseph is absent from the Canon. (And, in case you were wondering, there is no Third Confiteor).