Yes, the quote from Yuan Shi was only for Samarqand's submission of households registry and Yuan Dynasty's sending off tax collectors.
Most of the info in my post was translated from "陳高華說元朝" （Chen Kao Hua talks about the Yuan Dynasty) published in 2009. He is a retired professor of history who centred his research mainly on Yuan Dynasty and became one of the experts in that field. He was a member of an editorial board of U.N. for "The Civilization History of Central Asia". He was also used to be the president of the Chinese research society for Yuan dynasty history.中國元史硏究會
Ok, I see it. "命雪尼台铁木察使薛迷思干部。己未，升中政院秩从一品。辛酉，遣人使诸王察八儿、宽阇所。壬戌，太尉脱脱奏：“泉州大商合只铁即剌进异木沉檀可构宫室者。”敕江浙行省驿致之。癸亥，万户也列门合散来自薛迷思干等城，进呈太祖时所造户口青册，赐银钞币帛有差。"
"ordered Xuenitai tiemucha to be an envoy to Samarkand. ...in the year of Guihai, the head of the tumen, yeliemenhesan came from Samarqand, and presented the registry made during the time of Taizu （Chinggis)."
"Samarqand, Talas, Tashkend etc pays tax to the county officials every three years. Now, because Xuenitai tiemucha went there, they ordered Konchek (Khan of Chagatai， son of Duwa） to keep two years of that and give it to the collectors, and one year of that to present up (to the court at Beijing)."
The Yuan seem to have regained the ability to tax cities in the Chagatai Khanate such as Samarqand since Duwa's submission in 1304, albeit only a third of it, whereas Chagatai khans could also collect their tax in their fiefs in northern China.