"Saris" in this context indeed refers to the garment.
It might help to think of the three saris that the Ayah received every year to be a perquisite, rather than a part of her regular salary. It is customary in India, even today, to provide a small bonus to one's employees before important festivals. Most likely the bonuses that the Ayah received were in the form of saris rather than cash.
The Ayah would also not have to spend too much money on herself for new clothes if she was receiving three saris every year, so the arrangement probably suited her as well.
Some of the most important Tamil festivals include Pongal, Puthandu, Navaratri and Deepavali, and the Ayah probably received new clothes for some of these occasions. In fact, it is traditional to shop for new clothes for the entire family specifically to celebrate these festivals. One can expect the markets to be filled with fresh stocks accompanied by heavy discounts. It might very well have been cheaper and more convenient for the mistress to buy an additional sari for the Ayah along with the bulk purchasing before a festival.
Another point worth mentioning is that since the Ayah was residing under the same roof as her employers, the mistress would probably feel obligated to provide new clothes for the Ayah too when purchasing new clothes for the rest of the family, since she was a part of the household in a way. Certainly there would be an aspect of social pressure in creating such a sentiment, considering the unfavourable reaction in the family when the Ayah failed to return immediately from her trip to her home in Saidapet:
[Radha's] mother and others were furious. ‘She has perhaps been run over and killed,’ they said. ‘Such a blundering, blind fool. I am surprised it didn’t happen before. She must have taken it into her head to give herself a holiday suddenly. I will dismiss her for this. No one is indispensable. These old servants take too much for granted, they must be taught a lesson.’
It is also possible (but less likely, in my opinion) that the three saris the Ayah received every year were not bonuses for any festival, but were instead gifts of old saris belonging to the mistress that were still serviceable. It would be less wasteful to give them to the Ayah compared to throwing them away.