In preparing the printer’s manuscript for typesetting, the 1830 compositor, John Gilbert, supralinearly inserted in pencil the subject pronoun he before the dependent having-clause, probably because he did not want the reader to misinterpret the preceding pronoun they as the subject for having; obviously, the intended meaning is that Satan was the one subjecting those who had spiritually died. We have evidence that scribe 2 of 𝓟 occasionally omitted the subject pronoun he; for a list, see under Alma 11:2. So it is quite possible that Gilbert’s emendation represents the original text.
Although the he is helpful in Alma 12:17, the question is whether the he is necessary (if so, there must have been an early loss of the subject pronoun). There are examples elsewhere in the text of present-participial clauses that refer to nearby nonsubject words rather than to more distant subject noun phrases, as in the following examples:
The earliest text in Alma 12:17 is therefore possible. Consequently, the critical text will restore the earliest reading: “according to the power and captivity of Satan / having subjected them according to his will”.
Summary: Restore in Alma 12:17 the earliest reading, “according to the power and captivity of Satan / having subjected them according to his will”; the 1830 typesetter supplied the subject pronoun he, but this emendation was unnecessary since elsewhere the text allows such usage.