Start with this:
Prince Andrew shook his head.
That's a subject, a verb, and an object. Since there's only one verb, there's only one tense. Tense consistency isn't an issue.
We can modify "Prince Andrew" with a participial phrase. The following is a participial phrase:
looking again at that genealogical tree
The participle is "looking". As a participle, "looking" has no tense. When this phrase is added to the sentence above, tense consistency still isn't an issue:
Prince Andrew, looking again at that genealogical tree, shook his head.
The commas surrounding this long participial phrase are necessary. They have nothing to do with when the laughing happens. They have a lot to do with how long the phrase is, and they have a lot to do with the fact that the phrase follows the noun that it modifies.
Instead of modifying only the subject, we might choose to modify the entire clause:
Prince Andrew shook his head, laughing.
In this case, the comma seems optional. "Laughing" is only one word, and it's in the right position to modify the verb "shook". However, a longer participial phrase makes the comma much more useful:
Prince Andrew shook his head, laughing as a man with good reason laughs.
The laughter of a man with good reason isn't something that happens in the past. Well, in a way, it did. Such laughter happened in the past, is happening in the present, and will happen in the future. It is an eternal truth, occurring in the eternal now. It's little different than saying "God is good" or "Two plus two is four".
Also, if the "laughs" from "as a man laughs" (and, in the original, "looks") has to be made consistent with anything, it would need to be consistent with the participle "laughing". The rest of the sentence is all part of that participial phrase. Tense consistency with participles, of course, is impossible.