In Hindu mythology, the god of death is Yama. His attendants are called yamaduut, literally Yama's messengers (duut). The Bengali original of ছেলেবেলা / chhelebelaa uses the phrase যমের দূত / yamer duut, "the messenger of Yama", rather than the substantive যমদূত yamaduut, but the reference is the same. The word yamaduut is the same in singular and plural forms.
It's the job of a yamaduut to approach at the moment of death, tell the dead person that they are now dead, and escort the person's soul to the afterlife. Naturally yamaduut are much feared. Metaphorically, any person whose presence foretells calamity can be called a yamaduut.
The word translated "steward" is দেওয়ান / deoyaan, which is the Bengali spelling for dewan. A dewan was a revenue officer. So the question asked here boils down to: "why would the dewan of an indigo plantation be feared enough to be equated with a yamaduut?"
Indigo planting in India was notoriously exploitative. Farmers were persuaded to replace food crops with indigo. The indigo plants were sold to them on credit, the interest rates being such that farmers could never pay down the principal. The accrued debt was passed on to their heirs. Entire generations of farmers were in servitude to the planters as a result. Farmers also received a paltry sum for their indigo crops, amounting to only about 2.5% of the market value.
As the revenue officer of the plantation, the dewan managed the accounts with the farmers. He would be the one who paid the farmers for their indigo plants, but more importantly, he would also be the one to collect the interest due on the loans made, as well as the tax due on the cultivated land. Since the latter amounts typically exceeded the payment the farmers received, any dealings with the dewan were frightening.
The equivalence between a dewan and a yamaduut could often be quite literal: E. De-Latour, a witness before the British commission to look into the conditions of the indigo trade, testified that "not a chest of Indigo reached England without being stained with human blood". Conditions finally reached the point where the peasant farmers rebelled against the planters. The Indigo Revolt began in 1859, just a couple of years before Tagore was born. The revolt was successful, insofar as measures were laid out that marginally improved conditions for the farmers. But by the turn of the twentieth century, the manufacture of synthetic indigo became commercially viable. Indigo plantation in India, being no longer profitable, came to an end.
This passage from Tagore's memoir, written in 1940, recalls this history from about a half-century previous. The indigo factory still stands, but it isn't used to manufacture indigo any more. The white planters, their dewans, and the bailiffs who served as enforcers against the farmers have all disappeared. But Tagore remembers the toll the exploitative system took on the peasants, particularly the fear inspired by the dewans, so great that they were regarded as yamaduut or Death's henchmen.