Both manuscripts read “every man did go forth and offer up these same prayers”. The 1830 compositor accidentally mis-set these as the. The 1981 LDS edition, following the reading of the manuscripts, restored the original these. The critical text will, of course, maintain the original determiner. For further discussion regarding the tendency in the early history of the text to mix up these and the, see under Jacob 1:1.
Summary: Maintain in Alma 31:20 the reading of the original manuscript, “every man did go forth and offer up these same prayers”.