In this situation, I would ask two questions:
Do the two commas help clarify the meaning of the sentence?
Do they help establish the pacing that the writer wants to convey?
If I answered yes to the first question, I would include the commas. If I answered no to the first question but yes to the second question, I might still be inclined to add the commas, though I would recognize that the argument in their favor was somewhat weaker than an argument founded on syntactical clarity. If I answered no to both questions, I wouldn't add the commas—because at that point I would have failed to establish that including them served any practical purpose.
Consider this sentence:
The double play went 6-4-3, from Tinker to Evers to Chance.
I see no benefit in adding commas after "Tinker" and "Evers." The extra commas don't help readers follow the progress of the ball; they just slow everything down. But in terms of coherence, nothing really changes if we expand the sentence to say this:
The double play went 6-4-3, from shortstop Joe Tinker to second baseman Johnny Evers to first baseman Frank Chance.
Again the pacing of the ball movement is quick and sure, and commas wouldn't have improved the sentence's clarity and pace at all.
Now let's return to the original example, but with the second and third commas omitted:
From what I could see, Brom's facial expression turned from a neutral look to a surprised one and then to displeasure.
This is essentially "Tinker to Evers to Chance" all over again—but this time we're dealing with actions of less clear-cut duration. Was the look of surprise over in a moment? If so, perhaps the sentence would benefit from dropping not only the commas but some excess word baggage as well:
I watched Brom's facial expression shift rapidly from neutral to surprised to displeased.
On the other hand, if the surprise lingered, the sentence may have reason to linger, too, and adding a comma after the moment of surprise can help convey a sense of that gradual change:
From what I could see, Brom's facial expression turned from a neutral look to a surprised one, and then to a frown of displeasure.
The crucial point is that no syntactical necessity compels you to use commas to break out segments along a chain of motion—and often such commas aren't helpful at all. Why is this so? Because the segments involved in a motion progression do not form a parallel series—a syntactical structure in which segment-delimiting commas (with or without the Oxford comma after the next-to-last term) are necessary, as in this sentence:
"Three-quarters of the Cubs' infield consisted of shortstop Joe Tinker, second baseman Johnny Evers[,] and first baseman Frank Chance.
To the contrary, the serial segments in a typical "X to Y to Z" construction are logically (and often temporally) consecutive—not simultaneous as in a typical parallel series. You can include commas if you think that they will help readers navigate the sentence's circuit at the desired pace, but they are by no means required.
As a matter of fact, I had trouble thinking of any sentence of moderate size that would benefit from the presence of a comma between the "from" segment and the first "to" segment. The only relevant example I could come up with is one in which the "from" term contains a nested "to" that might be confused with the "to" that marks the start of the next segment in the sequence. Clearly, a comma is very helpful at the end of the "from" term in this construction:
The train ran from Waukesha to the west of Milwaukee, to Milwaukee itself, and then to Chicago to the south.
Without the commas to guide you, parsing that sentence would be a nightmare. But in most instances, the identity of each discrete consecutive segment is instantly clear without commas, and the only further element that you might want to to consider in deciding how to punctuate the sentence is the appropriate pacing.