All kittens, of any cat breed or no breed at all, are born with blue eyes and this is because the pigmentation in the iris is not fully formed which leaves the colour in the eyes to be created by the physical nature of what is called the refraction of light as it impinges upon the eye. There is a page on that on this website which explains how that works.
The Siamese is typical in that the kitten is born devoid of pigment and begins to form pigment within a few days. Accordingly, the Siamese cat will start off with blue eyes but they will change in colour as the pigment develops under the direction of the relevant gene. Normally in the Siamese, the colour of the eyes will start forming to blue after about 6 weeks.
It would seem to me that on some occasions, at this stage, a Siamese cat may develop odd-eyes (heterochromia iridum) or the wrong colour eyes per the breed standard. One eye may remain blue and the other may turn yellow. Normally, odd-eyes will be seen in a cat that carries the white spotting gene or the dominant white gene. However, the Siamese cat is a Siamese cat because it carries a specific gene and not as far as I’m aware the white spotting gene.
On that basis, when people talk about a change of eye colour in a Siamese cat, they may be referring to a Siamese cat which is not purebred. Sometimes you see Siamese-type cats with the odd fleck of white caused by the white spotting gene. These cats may have odd-eye color or the “wrong” eye color. I am happy be corrected or my post added to by anyone.