The issue is that the C memory model allows more behaviours than the memory model of x86-64 processors. You can thus write code which is incorrect according to the C language specification but will happen to work on x86-64 processors. Moving to arm64 (with its weaker memory model than x86-64) will then reveal the latent bug in your program.
And “happen to work on x86-64 processors” also will depend on the compiler. If you write
*a = 1;
*b = 'p';
both the compiler and the CPU can freely pick the order in which those two happen (or even execute them in parallel, or do half of one first, then the other, then the other half of the first, but I think those are hypothetical cases)x86-64 will never do such a swap, but x86-64 compilers might.
If you write
*a = 1;
*b = 2;
, things might be different for the C compiler because a and b can alias. The hardware still is free to change that order, though.
This architecture trick was often used for precisely this - finding bugs in the program that would work in one architecture and fail in another. A very common class of issues like these was about endianness, and PowerPC was very handy because it could boot as both high and low-endian modes (I think I remember different versions of Linux for each mode, but I'm no longer sure).