I assume that the Yom Taryanus occurred during the time that we had Bais Sheni. If that is so, would Purim not have already occurred and Taanis Esther on the 13th of Adar? If this is so how could the Yom Taryanus initially have been instituted (including no fasting) if Taanis Esther preceded it? Or, perhaps, was Taanis Esther suspended and then re-instituted due to the execution of Lulianus and Papus?
Your question is valid as to Yom Nikanor which was on the thirteenth of Adar (Yom Toryanus was on the twelfth). Obviously, it was declared in Bayis Sheni as you pointed out, which was after the institution of Ta'anis Ester.
Ran explains that Yom Nikanor was only in regard to Hesped and not to Ta'anis. Sefas Emes, however offers your explanation, that the fast was suspended for the years that Yom Nikanor was a Yom Tov.
Dov Zupnik