The question says "work," and that word is doing a lot. Does it mean the fungus is gone, or the nail looks normal again? The two do not arrive on the same date, and readers in Itasca deserve to know which one a quoted timeline refers to.
The answer in one line
A treatment can succeed and the nail can still look bad for a long time. MedlinePlus says that even if treatment is successful, it may take up to a year for a new clear nail to grow.
Reading that sentence closely
Two conditions sit inside it. "If treatment is successful" means the year is not a promise that the treatment worked. "May take up to a year" gives a ceiling, not a guarantee, and it counts the wait for a new clear nail rather than the length of the treatment itself.
So when a plan says results in a given number of weeks, ask what is being measured at that point: the fungus, or the nail.
The onychomycosis papers behind the timeline
The clinical background is laid out in the AFP article on onychomycosis, also called nail fungus and in Onychomycosis: Old and New on PubMed Central.
What to confirm, and with whom
Ask your podiatrist what "done" means for your treatment, when you will be re-checked, and what a follow-up visit is meant to measure.
The clause people skip
The year in that sentence is about the nail growing out clear, so ask your clinician to say what they will look for at each visit before the new nail has finished growing.