The dahi/yogurt I use in my Delhi restaurant is made from full fat water buffalo milk.
It is probably more than 10% butterfat and has a consistency somewhere between heavy whipping cream and toothpaste (I'm not kidding, you have to squeeze this stuff out of the packet!)
If I have to use some crappy American yogurt I'd pick full fat Greek style. Although US yogurt is so full of other nonsense I hate using it.
But if you insist on using a 'low fat' yogurt in an Indian dish mixing a little starch in the low fat product will keep it from splitting & help it to 'thicken' like it is supposed to.
Some 'starches' I've used for example-
1 tsp gram flour (besan) per cup of yogurt- beat it in before adding, has a nutty flavor, 'expands' & thickens, gives a yellow hue
1 tsp corn starch per cup of yogurt- beat it in before adding, remove dish from heat before adding, stir well before returning to heat or may 'clot, does not interfere with flavor or color so it's great if you want a 'white sauce like for Safed Maaz
2 tsp white flour per cup of yogurt- beat it in before adding, can dull flavor a tiny bit or taste 'pasty if not well cooked, tends to 'lighten' the color of the dish
As far as Rogan Josh goes-
Rogan Josh is a Kashmiri dish, my husband is Kashmiri. I can tell you Kashmiri's would NEVER put tomatoes in Rogan Josh, In modern Indian 'Rogan Josh' just means any curry with mutton & a red sauce. The red hue of authentic Rogan Josh comes from Kashmiri mirch (Kashmiri red chills) and Ratan Jot (flowers of the cockscomb flower).
But if you insist on making one of those less authentic 'Rogan Josh' recipes with tomatoes, add some starch to the yogurt before adding & it won't split.