Alnilam is only briefly mentioned in Allen:

"Alnilam, Anilam, Ainilam, and Alnihan are from Al Nithām, or Al Nathm, the String of Pearls, or, as Recorde said, the Bullions set in the middle of Orion's Belt.

It portended fleeting public honors to those born under its influence.

The spectrum is Sirian, and the star recedes from us at the rate of about 16½ miles a second.

It is the central one of the Belt, culminating on the 25th of January."

The word bullion made me associate to bull. But English Etymology:

"Bullion ... precious metal in the mass ... Rom. *bulliōnem boiling, f. L. bullīre boil ..."

It makes sense. When heat makes contact with water the result will be boiling. The Belt of Orion lies across the celestial equator.

Boiling causes everything to churn around and what is at bottom will suddenly be on the surface:

.. the whole sea is conscious of the rise of that star, as is most clearly seen in the Dardanelles, for sea-weed and fishes float on the surface, and everything is turned up from the bottom ...

Indeed it should portend only a 'fleeting public honor', because in an instant it once again will be submerged, no longer at the top.