There are two basic schools of thought about this principle cited by Rebbi Zeira.
The Talmud in Niddah 66a is the most primary source for the discussion of this.
אמר רב התקין רבי בשדות ראתה יום אחד תשב ששה והוא שנים תשב ששה והן שלשה תשב שבעה נקיים אמר ר' זירא בנות ישראל החמירו על עצמן שאפילו רואות טפת דם כחרדל יושבות עליה שבעה נקיים
Rav said: Rebbi established in the fields1 that a woman who sees once sits that day plus the following six, if she sees twice she sits that day plus the following six. If she sees thrice, she sits for seven [full] clean days. Rebbi Zeira said: The daughters of Israel were stringent upon themselves that even if they see a drop of blood like a mustard seed, they sit for seven [full] clean days.
I was intentionally vague in my translation to avoid matters of dispute.
Later in the Gemara, Rava says about this statement of Rebbi Zeira:
היכא דאחמור אחמור היכא דלא אחמור לא אחמור
Where they were stringent, they were stringent, and where they weren't, they weren't
In Berachos 31a, the practice of Rebbi Zeira is cited by Abaye as a "codified halacha"
והיכי דמי הלכה פסוקה אמר אביי כי הא דר' זירא דאמר ר' זירא בנות ישראל החמירו על עצמן שאפילו רואות טיפת דם כחרדל יושבת עליה שבעה נקיים
What is an example of a "codified halacha"? Like what Rebbi Zeira said, that the daughters of Israel...
In terms of why this practice came into being, the Ramban in Hilchos Niddah ch.1 writes that the stringency of Rebbi really addressed all concerns, but Jewish women wanted to make it simpler for themselves and just treat all blood-spotting the same, so they adopted the practice cited by Rebbi Zeira. The Ran, among others, points out that this stringency is not as extensive as it sounds, because the enactment of Rebbi already demanded 6 clean days for even one spotting. They only added one more day, the purpose of which was to make things simpler.
As to when it developed, note that Rava in Nidda 66a referred to the practice as being accepted in some places but not in others2. Abaye, a contemporary of Rava, cites it as an example of a "codified halacha" in Berachos 31a, the implication of which being that it is universally accepted and bears no further discussion. Therefore it seems that its transformation must have taken place during Rava's time (ca 270 - 350 according to this Wikipedia article stub), before Abaye passed away (339 according to this Wikipedia article). So approximately around the year 300. The Piskei HaRosh implies this understanding, as in HaTinokes Siman 4 he writes that based on Niddah 66a the practice was not widespread, but in Hilchos Mikvaos Siman 36 he writes that in the times of Rava it was widespread (Divrei Chamudos on Mikvaos note 6 makes this point).
As to how it developed, there are two basic schools of thought, as I mentioned.
The Ritva writes that the practice was initiated as a grassroots stringency which Jewish women accepted upon themselves. However, the Rabbis saw that it was fitting, and they adopted the practice as their own enactment. They basically co-opted the practice as their own formalized Rabbinic decree. Tosefos to Megillah 28b s.v. שאפילו רואות implies such an understanding, as he writes the following:
היאך מצינו טפה כחרדל הגורמת שבעה נקיים בדאורייתא דודאי לא תקנו חכמים דבר דלית דכוותיה דאורייתא
Where do we find a drop the size of a mustard seed that causes a Biblical requirement for seven clean days? Because certainly the rabbis would not have established something to which there isn't a Biblical parallel!
Tosefos seems to view this halacha as a formal Rabbinic enactment. Otherwise you cannot challenge the concept based on the Rabbinic methodology of its implementation. His words, "תקנו חכמים," further imply as much.
Others, however, have a much more passive approach. The Rosh writes in Tinokes Siman 6
עבדו רבנן הרחקה יתירה ונהיגו בנות ישראל כר' זירא
The Rabbis made a further removal and guided Jewish women to act in accordance with R' Zeira
and later he writes
החמירו על בנות ישראל
[They] were stringent on Jewish women...
The Maadanei Yom Tov note צ there writes that the Rosh was justified in calling it the stringency of the Rabbis, even though it was self-imposed, because once the Rabbis allowed them to do it, and set it as a "codified Halacha" it can be quoted as such.
The Ramban, Hilchos Niddah Ch. 1 halacha 19, writes
חומרא זו שנהגו בנות ישראל הוכשרה בעיני החכמים ועשו אותה כהלכה פסוקה בכל מקום, ולפיכך אסור לאדם להקל בה ראשו לעולם
This stringency which Jewish women followed was appropriate in the eyes of the Rabbis, and they made it like a codified halacha in all places, and therefore it is forbidden to be lenient with it, ever.
The Rambam writes in Hilchos Issurei Bi'ah 11:10:
חומרה יתרה שנהגו בה בנות ישראל מימי חכמי תלמוד; ואין לסור ממנה, לעולם.
[This] is an additional stringency which Jewish women practiced over the times of the Rabbis of the Talmud, and one may not depart from it, ever.
The Rambam makes no mention of it ever evolving to more than an accepted practice.
Following the first train of thought, there is very little room to view the practice any differently than any other Rabbinic enactment. However, the second approach allows the room for such discussion, and indeed the Galya Masechta writes that since it is a matter of custom, there is room to be lenient with Rebbi Zeira's halacha under pressing circumstances. R' Shlomo Zalman in Minchas Shlomo Tinyana 72 argues with the Galya Masechta and says that despite its origins, it has the full weight of a Rabbinical law.
1 Rashi explains that "in the fields" means a place where there weren't Bnei Torah, and therefore the women did not know how to count their cycles properly. The Ramban (in Chiddushim to Niddah 66a) explains similarly, adding that they didn't know how to identify pure vs. impure blood. The text of the Rif had בסוודות, and the Me'iri had בשוריית, which refer to specific places, although the Ran in Sh'vuos has the same explanation as Rashi on the text of the Rif. It would be possible to discuss limiting the enactment of Rebbi to places without Bnei Torah based on this. However, the Rambam, the Ramban, and the Tur all make no mention of any limitation to Rebbe's enactment, and indeed the Ramban and Tur both provide justification for the enactment which is all-encompassing.
2 Although some understand this to be referring to the application of the stringency to birth, as per the context of the Gemara there, and not to the universal nature of its acceptance.