He (Martinez) didn't, so what is it? Keep addition as is, but be willing to change the usual rules of multiplication in order to impose the new sign rule: (-) x (-) = (-).
He seems to have invented something altogether different than the "sign" we know. So I don't think it is correct to compare "rules" just because the two systems use the same symbol. In his system, the minus sign would equate to what we call "i".