Hmm. To me, it seems that ISRO has done something new and innovative with the CE-25 crogenic stage. something that has not been done anywhere else as far as I can see. I will come to that in a bit.
The thing about all this separation and "slosh" and "ullage" / whatever ,bit is this. As long as the the engines are firing, there is a clear liquid surface that is formed (the cork floats in the water), and there is no issue what so ever. So what happens when the thrust is turned off for whatever reason ? The vehicle is coasting under it's own inertia under the effect of earth's gravity. In effect, this is in Free Fall
. From high school physics, we know that a freely falling body (like the rocket in this condition, or approximately when we are in a roller coaster /giant wheel in it's downward leg as most kids know and feel, or a satellite in orbit) is weightless
(this is not either microgravity or g = 0) . Now under conditions of weightlessness (ie coast with engines off in a rocket), the liquid fuel , since it is now weightless, will have surface tension effects predominating ( like the photos and videos we are all familiar with of water forming into spheres in space etc..and no, you dont need to go to "Vomit Comet" to do that, just putting a plane into a free fall and holding a cup of water will make that happen).
So obviously in such conditions, if you want to start the liquid engine (either for the first time if staging, or restarting while coasting), you need to find someway of making the liquid fuel behave "normally" like in a non weightless condition. The easiest way is to give it a momentary acceleration and the surface is instantly formed again and the liquid is as "normal". You can have things like springs separating the stages giving the "kick" (heavy, inefficient,can be done once), or you can have ullage motors, small motors that give the same small kick (either solids or gas based jets etc) , or if you really want multiple starts more complex schemes like confining some of the fuel and oxidizer into small tanks that are kept full and then pressure fed into the chamber etc.
How does all this work in practice ? There are two ways to go about it. ie ensuring that the thrust is always on, and you have ullage problem in the first place and the second is to manage the ullage. During stage separation , this gives rise to two schemes, a) Parallel staging, where there is an overlap in the of the firing of the two stages so that thrust is always on b) Tandem staging , where the previous stage gets separated , the vehicle coasts for a few seconds and then the next stage fires when there is enough separation between the spent stage and the vehicle.
Now in the lower strap on booster stages, the parallel staging is quite obvious. There is overlap in firing, thrust is always on, and the core stage (even if liquid like in the Ariane V) fires even in mid air without any issues. It is in the 2nd stage and higher that is interesting. The Russians went about it with their R7 / Soyuz and derivatives very elegantly. They basically put the inter-stage in a truss, so that they could simply fire the next stage engine (the exhaust flows out through the space truss) , just as the previous stage engine tails off and the stage separates "hot" , and you achieve parallel staging and avoid the ullage business totally during separation. In addition, you have enough control forces at hand since the engines are thrusting to control the vehicle.
The Chinese Long March
(the blow up diagram of their launch sequence is interesting) and our GSLV MK2 in the cryogenic stage and also our Agni missiles use the R7/Soyuz kind of staging. That is the reason the GSVL Mk1/2 wont need separation motors for their cryogenic stage. The American vehicles, like Saturn V had mostly tandem staging (as they had a solid skirt in their inter stages)and would have needed separation motors during staging and it would needed a few seconds gap for the bell/nozzle of the stage to clear the skirt before the next stage could fire.