Vowing to fast on a particular day creates a commitment of the person making the vow. Yet if the Lawgiver has left a broad choice of days for a Ramadan make-up fast, a personal vow does not automatically remove that breadth.
For example, a person vows to fast on Thursday but intends a make-up or expiatory fast on that day. The text allows that fast to be counted for the make-up or expiatory duty because the law did not assign those obligations to one fixed day.
Whether and how the separate liability arising from the vow remains to be discharged is a distinct question governed by the relevant details.
Rule: personal commitments operate within the law; they do not alter the basic requirements enacted by the Lawgiver.