"In that time" means he's talking about a future event. "A people terrible from the beginning," in the beginning of the history of Israel as a nation, they swept over Canaan by divine decree and destroyed all the nations. See also D&C 128:24.
"meted out", they are measured out, chiseled at, little by little their borders are overcome until they are overrun, "and trodden under foot."
The final destination is the temple, the "place of the name of the Lord."