Yes, the correct form is aurifer, though in early Old Latin it would have been *auriferos (actually *ausiferos), as you'd expect.
For second-declension nouns with stems ending in r (original r, not rhotacised s), there was a rule in late Old Latin saying the ending -os of the nominative singular would be lost in certain cases (and if that meant the word ended in a consonant + r, an epenthetic -e- would be inserted). According to Michael Weiss' Outline of the Historical and Comparative Grammar of Latin, those cases are:
- If a consonant precedes -ros (Old Latin sakros > Classical Latin sacer 'sacred').
- If a vowel precedes -ros and the word is at least trisyllabic with a short penult (vesper 'evening' < *vesperos and līber 'free' < *loiberos, but ferus 'wild' and sincērus 'sound, whole').
- The word vir 'man', which may be analogical to puer 'boy', gener 'son-in-law, socer 'father-in-law'.
In all other cases, the -os is regularly preserved (and -os regularly became -us around the 3rd century BCE). Aurifer falls under the second case, and Tibicen auriferus got its name from a modern scientist who misapplied analogy.