JOEL - Actually the Lord created only one "universe", but many galaxies and worlds, which are populated with His mortal children, as on our planet. Other "universes" have been and will be created by other Gods.
Your question is news to me. I too was always taught that all of God's children, regardless of which planet they live on, will have the opportunity to be exalted to Godhood. And that the only reason why Jesus came to this planet is because it was the most wicked of all of His creations(Moses 7:36).
Joseph Smith received revelations explaining that through Jesus Christ, many worlds are created and inhabited (D&C 76:22-24; 93:9-10; Moses 1:33).
A poetic version of D&C 76:22-24, written by Joseph Smith, lends support to the fact that Christ's plan of salvation and atonement includes inhabitants of all worlds:

"And now after all of the proofs made of him,
By witnesses truly, by whom he was known,
This is mine, last of all, that he lives; yea he lives!
And sits at the right hand of God, on his throne.
And I heard a great voice, bearing record from heav’n,
He’s the Saviour, and only begotten of God—
By him, of him, and through him, the worlds were all made,
Even all that career in the heavens so broad,
Whose inhabitants, too, from the first to the last,
Are sav’d by the very same Saviour of ours;
And, of course, are begotten God’s daughters and sons.
By the very same truths, and the very same pow’rs."
(Times and Seasons, 4:82-83, stanzas 18-20)

The inhabitants of these other planets are children of God and are created in His image, though they might differ from the earth's inhabitants, according to how far they have progressed in the mortal sense. (Moses 1:33; D&C 76:24).
But regardless of what developmental stage they are in, the whole plan of salvation and exaltation was made known to all of us in the pre-mortal life, and we all agreed to follow it, regardless of which planet we eventually ended up on. All beings of all inhabited planets will have been taught and had the chance to accept the Gospel of Christ. Each inhabited planet will experience the same changes from a telestial to a terrestrial, and finnaly to a celestial state, the same as our planet (D&C 88:18-19). Revelation received by Joseph Smith suggests that resurrected beings will reside on their own celestialized planets (D&C 130:4-7).

According to the Encyclopedia of Mormonism:
"The means of salvation through the gospel of Jesus Christ is the same for all of God's creations. Creation is continual and expansive and is directed toward the eternal happiness of all intelligent beings, for the Lord told Moses, "As one earth shall pass away, and the heavens thereof even so shall another come; and there is no end to my works, neither to my words" (Moses 1:38). For Latter-day Saints the gospel of Jesus Christ has universal validity, in both time and space. God's Plan of Salvation operates on a universal scale. Latter-day Saints believe that there are now countless planets whose inhabitants—children of God—are progressing, as are human beings on this earth, according to eternal principles towards a Godlike life." (Encycl. of Morm.)

God is no respecter of persons (D. & C. 1:35; 38:16), meaning that every person who complies with a law (which we all agreed to do in the pre-mortal life), receives the blessing ordained to attend such obedience. Why then should we be the only ones who can be exalted, just because we happen to live on a different piece of rock in space? Jesus came to this one, only because He knew that the inhabitants would be wicked enough to crucify Him, so that He could bring forth the atonement and thus continue the plan of salvation.
So your thinking was correct. "The Lord's plan was designed to exalt all His worthy posterity". So whoever told you that only inhabitants of this planet will have the chance to become gods, needs to check their references and be sure that they have not misunderstood the concepts.