Is the self RAM used in the RL78 family libraries need to be initialized?

The self RAM area used in the library need not be initialized in the user program because the RAM is initialized by the initialization function of the library*.
However, if the user program uses the self RAM area for the library, make sure that the user program initializes that area.

*Note: If you are using v2.20 or an earlier version of Flash Self Programming Library Type01 and more than 1 Kbyte of self RAM is required, the user program will need to initialize the 10-byte range of addresses beyond the first Kbyte because the library does not.