Per the chronology:
- On January 25, 2023 [..] NHTSA advised Tesla that it had identified potential concerns related to certain
operational characteristics of FSD Beta in four specific roadway environments [..] NHTSA
requested that Tesla address these concerns by filing a recall notice.
- In the following days, NHTSA and Tesla met numerous times to discuss the Agency’s concerns and Tesla’s
proposed over-the-air (“OTA”) improvements in response.
- On February 7, 2023, while not concurring with the agency’s analysis, Tesla decided to administer a voluntary
recall out of an abundance of caution
So yes, it was voluntary in the sense of "you don't want us to force you to do it" and it was indeed the NHTSA testing.