Translation: "people with upright eyes will arrive"
Excerpt from 《汉书》卷二十六《天文志》：

　　哀帝建平元年正月丁未日出时，有著天白气，广如一匹布，长十余丈，西南行，讠雚如雷，西南行一刻而止，名曰天狗。传曰：“言之不从，则有犬祸诗妖。”到其四年正月、二月、三月，民相惊动，讠雚晔奔走，传行诏筹祠西王母，又曰“从目人当来。”十二月，白气出西南，从地上至天，出参下，贯天厕，广如一匹布，长十余丈，十余日去。占曰：“天子有阴病。”其三年十一月壬子，太皇太后诏曰：“皇帝宽仁孝顺，奉承圣绪，靡有解怠，而久病未廖。夙夜惟思，殆继体之君不宜改作。《春秋》大复古，其复甘泉泰畤、汾阴后土如故。”

从 == 纵 == upright. As for who 纵目人 really was or were, there are a few hypotheses.
蜀人
The most prominent reference of 纵目 is related to 蜀人. It's said that either their first emperor, or the people themselves, were in possess of 纵目:

有蜀侯蚕丛,其目纵,始称王。——晋 常璩 《阳国志·蜀志》
蜀之先称王者,有蚕丛、柏濩、鱼凫(蒲泽)、开明。是时人萌,椎髻左衽,不晓文字,未有礼乐” ——西汉 杨雄 《蜀王本纪》

Then strange bronze masks unearthed from 蜀 area, current 四川 province. And they do possess extraordinary eyes. First, they are slightly larger to the east Asian standard, second, they are eerily protruded like that of a crab or shrimp.

It's probably that 蜀 people, being in a different ethnicity group, did have somewhat different eye shapes, or they do strange makeups of tattoos around their eyes. But I don't think 汉书 is referring to 蜀人 here, because 蜀 was already part of Han dynasty.
道教神祗
Since 西王母 was mentioned, it is possible that it was a reference to some evil deity, who would come and wreak havoc among the people, or some good deity who serves 西王母, and would come and save the people from suffering. We cannot know for sure.
There is a Taoism deity called 杨戬, who is said to have 纵目:

二郎为蚕丛之后，故其目纵。——道书《灌江备考》

杨戬 belongs to the good side, and he is also said to be 西王母's nephew. These were later stories, we really don't know originally what it was.
Tales about 杨戬 was first prominent in 蜀 area, then spread all over the country. Late depictions of 杨戬 shows him with one extra eye placed vertically between eyebrows. Early references doesn't seem to mention anything specific about his eye.
不知道
I found the two theories utterly implausible. If you see a man with an extra vertical eye in the middle, you would immediately think &quot;three eyes!&quot; instead of &quot;vertical eye!&quot; If it's a rumor about an invasion you would call them by race. If it's about deities then they ought to have names instead of a nickname.
What I observe is an alien invasion. They might be scary monsters that look like this: