What does mean by "to step aboard by [someone]"?

I know that "aboard" is a preposition as well as an adverb. It denotes:

on or onto a ship, aircraft, bus, or train: Cambridge Dictionary

Example sentence:

• The ship sank, killing 155 people aboard.
• I climbed aboard a ship.

But saying 'step aboard by [someone]' makes me doubtful to whether it means with someone or towards someone. Following is the excerpt from where I found the usage of 'by' and 'aboard':

THE HISPANIOLA lay some way out, and we went under the figureheads and round the sterns of many other ships, and their cables sometimes grated underneath our keel, and sometimes swung above us. At last, however, we got alongside, and were met and saluted as we stepped aboard by the mate, Mr. Arrow, a brown old sailor with earrings in his ears and a squint. He and the squire were very thick and friendly, but I soon observed that things were not the same between Mr. Trelawney and the captain.

Hence, what does the author mean to say? Do the narrator steps into the ship with the mate namely Arrow?

Solution 1:

we got alongside, and were met and saluted as we stepped aboard by the mate, Mr. Arrow

We were saluted by Mr. Arrow as we stepped aboard the Hispaniola.

Mr Arrow is the captain's mate of the Hispaniola.

We (got alongside, and) were met and saluted (as we stepped aboard) by the mate, Mr. Arrow