I have no experience with modern quarter-turn taps as I prefer the ease and economy of traditional tap washers. I do have lots of experience with O rings of various types.

Most commonly O ring breakage is due to the wrong size being used - diameter and/or section. when machined metal parts are fitted together and sealed with an O ring the clearance between the parts is very small - just enough to allow a sliding fit. The O ring(s) generally locate in a groove, sometimes on the end face but mostly around the diameter.

O ring sizes are chosen to completely fill grooves on the end face without either stretching or compressing the rubber. Grooves around the diameter require similar consideration though some stretching is needed to assemble them; once fitted the rubber should not be under either tension or compression. The chosen section of the ring will allow the groove to be filled when the components are fitted together therefore when they are separated it will seem the O ring is too thin for the groove. If the correct size is used with carefully machined components and suitable lubrication applied during assembly there should be no difficulty.

O rings are available in a number of different materials from soft natural rubbers to fairly hard synthetic materials.

I suggest you carefully measure the components and compare your results with the supplied O rings.

Use a tap reseating tool before installing the cartridge to ensure a square surface for the "O" ring to seat on
do not use any lubrication as that allows the pressure to push the "O" ring out and break it
tighten the cartridge in fully before using the lock ring to retain it