The Fortran-compiled List Programming Language (FLPL) had the functions XCARF and XCDRF. It doesn't look like MacCarthy and Russel invented CAR and CDR; they just stripped X...F from FLPL's notation.
IPL also used the same list structure; it used the terms SYMB and LINK.
That's the legend, but they're actually no such instruction mnemonics.
The Address and Decrement terms and the fields of the 36-bit word they denote do come from the architecture.
There are instructions like LXA and LXD -- load index from address, load index from decrement.
probably there were no such machine-level instructions, but assembler macros
The page doesn't say that these were predefined assembler macros provided by IBM. I'm tending toward the interpretation that the Lisp guys themselves (likely Russel) wrote these macros as part of the assembly language implementation of the interpreter. Which means they specified them to the assembler, rather than the other way around.
The names CAR and CDR weren't invented for Lisp or FLPL. They came from assembly language mnemonics on the IBM 704, where the first Lisp interpreter was implemented.
The original Lisp CAR and CDR operations used the machine-level instructions with those names on the IBM 704.
Cons cells were stored in single words of the 36-bit memory and 36/38-bit registers, and the CAR and CDR operations accessed the "address" and "decrement" 15-bit parts of a word, respectively.