"Mottling" as in the color in certain breeds like Ancona--yes.
Effect of the "mottling" gene--not quite.
Mottling seems to make white tip, black section, then the other section whatever color it normally would be (black on "mottled" breeds like Ancona, gold on Millie Fleur, dark red on Speckled Sussex, etc.)
The picture you post shows the white tip, the black part behind the tip, and then another color on the rest of the feather (gray in that picture.)
https://www.sciencedirect.com/science/article/pii/S0032579119355154
There's a link on that page to download the whole .pdf, too
The paper is titled
"The Mottling Gene, the Basis of Six Plumage Color Patterns in the Domestic Fowl"
and is by R.G. Somes, published 1979
That paper established that "mottling" (white tip on black feather) and "Mille Fleur" (white tip, black band, gold feather) and some others are indeed caused by the same recessive mottling gene. They discuss how the gene works, and they also crossed varieties to create a silver-mottled bird (similar to Millie Fleur or Speckled Sussex, but with silver instead of the gold.) They have various photos and diagrams in the paper.
Mille Fleur is one of the colors known to be caused by the mottling gene, the same one in that paper I just cited. So I think you are probably working with the usual mottling gene, but it looks different on different backgrounds--like Silver Duckwing.
That would require that Squeakers' father (Phoenix x Silver Duckwing OEGB) must have had one copy of the mottling gene.