I looked for the meaning of アフレコ in Jisho.org and after the meaning (dubbing) it says "Abbreviation, Wasei, word made in Japan". So since the word apparently it doesnt come from a foreign language, and since the dubbing process is a little over 100 years old, where does the word アフレコ come from?
アフレコ is an abbreviation of "after recording" (source: 三省堂 スーパー大辞林).
"wasei" literally means "Japanese-made". It's a term used to describe words that were made in Japan, despite being made out of foreign words. For example, "wasei eigo" means "Japanese-made English".
Another famous example of wasei eigo is "salaryman", which despite seeming like an English word, is only used in Japan. (Apparently not quite! See Eiríkr's comment.)