Christ tells the people that all that have received him have become sons of God. The past tense here indicates that this is a reference to a promise fulfilled in the believers in the Old World. However, it also comes as a remembrance of the foundational covenant of the people of Christ from the time of King Benjamin:
Mosiah 5:5-7
5 And we are willing to enter into a covenant with our God to do his will, and to be obedient to his commandments in all things that he shall command us, all the remainder of our days, that we may not bring upon ourselves a never-ending torment, as has been spoken by the angel, that we may not drink out of the cup of the wrath of God.
6 And now, these are the words which king Benjamin desired of them; and therefore he said unto them: Ye have spoken the words that I desired; and the covenant which ye have made is a righteous covenant.
7 And now, because of the covenant which ye have made ye shall be called the children of Christ, his sons, and his daughters; for behold, this day he hath spiritually begotten you; for ye say that your hearts are changed through faith on his name; therefore, ye are born of him and have become his sons and his daughters.
The Nephite gospel was embodied in this covenant. While the covenant originally signified an entire people, it was preserved in the church, and was renewed in the baptismal covenant. Thus even these people in the New World can be fulfillment of the promise to become Sons of God.