Brown stains on toilet paper do not necessarily make a woman niddah, but she should consider herself niddah until she clarifies her status. You correctly conducted yourself as if you were niddah from the beginning. However, your five-day minimum wait and veset calculations are not affected for several reasons.
Saturday night after sunset and Sunday morning until sunset are the same day according to the Jewish calendar. Thus, both the stain you found on Saturday night and the bleeding that you saw Sunday morning occurred on the first day of the Jewish week, and Sunday is day 1 of your five-day wait.
Note that when a woman considers herself niddah when she is uncertain of her status, that time can be counted toward her five-day wait. If, for example, you had found the stain on Shabbat during the day, and (because of your uncertainty) you had conducted yourselves as if you were niddah from then until you actually became niddah Sunday morning, then Shabbat would have been your day 1 of the five-day wait.
For the purposes of veset calculations there IS a difference between the night onah (sunset to sunrise) and the day onah (sunrise to sunset). However, what you saw on Saturday night does not factor into your veset calculations, since it is the beginning of the menstrual flow which marks the onah, which for you was Sunday daytime.
Premenstrual staining can create a veset haguf, a veset linked to bodily symptoms. Therefore, you should observe an onat perishah if you again begin to stain around the time you are expecting your period. Since the flow began one onah after the staining started, you should observe a veset the onah after staining starts. We also advise abstaining from relations from the time staining begins, as a precaution against a flow beginning earlier than expected.
Updated 8 August, 2023.