Nisaa
It depends on what the blood actually is, not on the fact that a pill is involved. If it carries the characteristics of menstrual blood, it is hayd and the fast breaks that day. If it is light spotting or staining without those characteristics, it is not hayd, and the fast stays valid.
The test scholars use here is the same one used for any bleeding whose nature is not obvious, and it does not change because a hormonal pill caused it. The Prophet (Salla Allahu Alayhi Wa Sallam) said to Fatimah bint Abi Hubaysh: “When it is menstrual blood it is dark and recognizable, so when it is like that, then stop praying, and when it is otherwise, do wudu and pray, for that is from a vein.” (Narrated by Abu Dawud and al-Nasai; classed as sahih by Ibn Hibban and al-Hakim). Blood carrying those qualities, dark, thick, with a distinct odor, is hayd whatever brought it on, whether it arrived on its own or broke through a pill taken to delay it.
Spotting that does not carry those qualities sits closer to sufrah and kudrah than to hayd itself. See are sufrah and kudrah part of hayd for Ibn Taymiyyah's reasoning: only blood with menstrual characteristics, appearing at a time associated with menses, counts as hayd, and anything lighter does not. That is the same lens that applies to the breakthrough spotting some women notice on a hormonal pill taken to delay their period. On its own, without the color and thickness the hadith describes, it does not break the fast.
Timing works in the same direction here. Istihadah is bleeding that does not match menstrual blood's characteristics or fall at the usual time of the period, and a delay pill is taken for the specific purpose of moving that usual time out of the way. The hadith of Hamnah bint Jahsh (Radi'Allahu Anha), who was told to treat her known cycle length as her hayd and the rest as istihadah (Narrated by Abu Dawud and al-Tirmidhi), is why scholars weigh a woman's known pattern alongside the blood itself rather than the blood alone. Spotting that shows up in the very days a pill is meant to hold her period off, without the characteristics of real menstrual blood, fails both tests: it neither looks like hayd nor falls where hayd was expected.
If the bleeding does turn into full hayd, whether right away or partway through the day, her fast breaks the moment it starts, even minutes before Maghrib, and that day is made up after Ramadan like any other day missed to hayd. Nothing about having taken a pill changes that; the ruling follows the blood, not the reason it appeared.
There is one more line worth knowing, and the four madhabs draw it in two places. Bleeding that continues past hayd's recognized maximum, ten days for the Hanafi school, fifteen for the Shafi'i, Maliki and Hanbali schools, is istihadah by definition regardless of how it looked when it started; see what counts as hayd for where each school sets that line and why.
Whichever it turns out to be, the practical routine is already settled either way: istihadah does not stop the fast any more than it stops prayer, so a diagnosis of istihadah simply means fasting continues with the same pad-and-wudu care istihadah asks for elsewhere. Because the whole point of a period delay pill for Ramadan is to avoid losing a single fast to hayd, this is exactly the kind of pattern worth logging as it happens rather than recalling weeks later; a period tracker built for Muslim women that records the blood's color and thickness on the day itself is what turns this into a short question for a scholar instead of a guess made from memory.