Yoghurt added to a hot dish frequently separates into grains suspended in a watery liquid. The cause is a protein behaviour that can be prevented, and every traditional method does so in the same way.
Yoghurt is already a fragile protein structure
Fermentation acidifies milk, which causes its casein proteins to lose their mutual repulsion and settle into a loose network that holds water throughout.
That network is what gives set yoghurt its body, and it is being maintained close to the point at which it would collapse further.
Adding heat supplies the energy needed to push the proteins past that point, so they draw together tightly and squeeze the water out as visible whey.
Acid and salt push in the same direction
Any additional acid in the dish, from tomatoes, tamarind or lime, lowers the pH further and makes the proteins more prone to clumping at a given temperature.
Salt has a related effect, altering the charges that keep protein particles apart, which is why salting a yoghurt-based sauce early increases the risk.
Combining heat, acid and salt is exactly the condition that curdles milk deliberately in cheese making, so a splitting gravy is that process happening unintentionally.
Starch physically blocks the proteins
Stirring a spoon of flour, gram flour or rice flour into the yoghurt before it goes in coats the protein particles and gets between them as they try to aggregate.
The starch granules also absorb water and thicken the surrounding liquid, which slows how quickly proteins can move towards each other.
This is why so many traditional yoghurt-based dishes include a pulse flour in the method, and why omitting it as an optional step causes the failure.
Temperature control does the rest
Whisking yoghurt smooth before adding it removes the existing clumps that would otherwise act as starting points for larger ones.
Tempering, by stirring a little hot liquid into the yoghurt before returning the mixture to the pan, raises its temperature gradually rather than shocking it.
Keeping the pan below a rolling boil afterwards, and stirring in one direction rather than agitating hard, keeps the network intact for the rest of the cooking.
Fat content and age both matter
Full-fat yoghurt splits less readily than low-fat, because fat globules physically separate the proteins and dilute the network.
Older, more acidic yoghurt splits sooner, so a batch that has been in the refrigerator for a week behaves differently from one set the previous day.
Where a dish is intended to have a smooth yoghurt body, the choice of yoghurt is therefore part of the recipe rather than a detail left to the shopper.