You can think of one picture holding all three uses: a figure tipping a jar so that water pours out. That figure was first traced in the stars, then borrowed as one of the twelve dated boxes of the zodiac, and finally used for the people whose birthdays fall in that box.
From the word’s history
Latin aquarius means water carrier, from aqua (water) plus -arius; it is a straight rendering of Greek Hydrokhoos, the water pourer, and the figure traces back to depictions of the Mesopotamian god Ea with water pouring from his shoulders or vases.
拉丁文 aquārius 是「提水的人」：aqua（水）＋ -arius。它照著希臘文 Hydrokhóos（倒水者）直譯過來，而更早的人形，來自美索不達米亞的神 Ea——圖像上水從他的肩膀或瓶子流下。所以「倒水」這個畫面，是名字本身就帶著的，不是後人硬配的。
Wiktionary entry Aquarius, etymology_text supplied in packet (source_ref kaikki:3f6f69a190036ae4:453618457:42438)
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