The neighbor is 25cm lower and sees us obligated to take measures

How to build and compact is one topic. Not of interest here. YOU build higher (than the original) and therefore you must also ensure that no water from your property flows onto the lower (and thus normal) lying property. So yes, the neighbor is completely right.

How high the house is built is initially irrelevant. It is about whether you have filled up the ground, for example, to access the terrace door at ground level. If you have filled up the natural slope by 40 cm towards the neighbor, you must ensure that your surface water (=rain) soaks away on your property and does not flow towards the neighbor.

What your neighbor does on their property is completely irrelevant.