The source I got this from (whom I consider to be of the highest reliability) stated that the first and second use a slower-burning NEPE compound than the third stage.
I am almost certain that your source was talking about the DF-41 successor or new silo based missile which is the "DF-NG, DF-51, DF-45" or whatever name it maybe that was under development before 2010, but may have finished today.
There were two papers. 1. 二十一世纪航天科学技术发展与前景高峰论坛暨中国宇航学会第二届学术年会论文集 published in 2007. The conference was held in 2006. 2. N15类高能低特征推进剂在战术导弹发动机上的应用研究 published in 2005. Since their date matches closely I believe they can be support one another. So I will list my points based on both of them.
- There is a conceptual design of advanced solid motor whose 1st stage is HTPB. 2nd stage being either N-15/N-15B or HTPB. 3rd stage being another type of unnamed high energy propellant.
- N-15 was used by strategic missile at the time. But the publication did not say all stages.
- N-15B is equally energy dense as N-15 but cheaper. It was under testing.
- The publication said "N-15B may be an option for future large solid motor".
- The unnamed propellant has 5% higher specific impulse than N-15. It will be used for 3rd stage for future strategic missile.
- N-15B is more retarded which was quoted as the other reason for its development besides being cheaper.
Point 1 is essentially saying that the then under-developing strategic missile is similar to MX using HTPB for 1st stage and maybe 2nd stage as well. This also agrees with point 2 as N-15 being used but not the whole missile.
Point 3 is probably about the then future missile aka DF-XX/45/51/NG. This missile may use yet another type of propellant for its 3rd stage as point 4.
N-15 is not to be used for all stages may be due to its higher price, or maybe due to its less ideal (than HTPB) handling property. We can never know for sure. If NEPE was so ideal, I would have expected that MX' being gradually refreshed with NEPE. But that we probably will never know.
All I have been saying is that, at least for China, all sorts of propellant and solid motors are made by same suppliers. There is not much division between military and civilian applications in terms of technology or producer, the only consideration is price, which is equally considered in missile and rocket launcher.
As of why some people have the idea that HTPB/APCP are better for civilian application (basically taking the cue from US example), I dare to say that if US is confident in NEPE and its price tag allows, US would have switched to full NEPE for SRBs. Not switching may be simply that they don't have their cheaper version of NEPE, the N-15B equivalent, nor do they have the volume of order to warrant the switching even if it is feasible.
I will stop here now as it is getting off topic.