If it was AIX, it wasn't a mainframe. AIX runs on IBM's POWER systems, which are their "midrange" line. (There was, for a brief time, AIX for S/370 I believe... but that disappeared long ago.)
Mainframe would be a System z (the S/360->S/370->S/390->z/Arch lineage), typically running z/OS (or Linux for z!)
And it isn't the same as AIX. IBM has two alive commercial UNIXs, which is kinda wild.
If there's any optional part of POSIX, it's not in there. You only get the 'MUST' parts of the base spec. No optional extensions, etc. When you're porting over C code to z/OS USS, you are often surprised when things you assumed were just part of every POSIX implementation aren't there. Fun times for all!