Cornelius Hispanus speaks of the carnifex stepping back as he pushed the condemned woman off the Tarpeian Rock. The word carnifex literally means “maker of meat”, but according to the OLD it was not used of an ordinary butcher; its primary meaning is executioner.
The Dictionary of Greek and Roman Antiquities (John Murray, 1875) provides this definition:
CA′RNIFEX, the public executioner at Rome, who put slaves and foreigners to death (Plaut. Bacch. IV.4.47; Capt. V.4.22), but no citizens, who were punished in a manner different from slaves. It was also his business to administer the torture. This office was considered so disgraceful, that he was not allowed to reside within the city (Cic. Pro Rabir. 5), but he lived without the Porta Metia or Esquilina (Plaut. Pseud. I.3.98), near the place destined for the punishment of slaves (Plaut. Cas. II.6.2; Tac. Ann. XV.60;Hor. Epod. V.99), called Sessorium under the emperors (Plut. Galb. 28).
The information about the duties of a carnifex is not consistent with his presence at the execution of a Vestal. Since this information is drawn from Plautus, who lived in the late 3rd and early 2nd centuries BCE, it may be that the duties had changed by the time of Seneca. Indeed, in Epistle 4.11, Pliny, writing in the late 1st century CE, mentions that a carnifex was present at the entombment of a Vestal.
I wonder if much would change with a public executioner: the Romans are fairly conservative with religious matters, and executing someone for their crimes was a matter the gods were concerned with. Things might stay fixed around some executions, while changing with the advent of the arena as a place for mass executions.
And not particularly relevant, but Cicero used to call Augustus a carnifex adulescens.