As there is no Adhan on 'Id-ul-Fitr, so you should not pronounce it. Ibn Zubair did not pronounce Adhan on that day. He (Ibn 'Abbas) also sent him (with this message) that sermon (is to be delivered) after the prayer, and thus it was done. So lbn Zubair observed prayer before Khutba.
The Absence of Adhan on Eid al-Fitr
The hadith establishes that no Adhan (call to prayer) or Iqamah (second call immediately preceding prayer) is to be pronounced for the Eid prayer. This is the established Sunnah, distinguishing it from the five daily obligatory prayers. Ibn Zubair's action confirms this practice among the Companions.
The Sequence of Prayer and Sermon
The narration clarifies the correct procedure: the Eid prayer is performed first, followed by the Khutba (sermon). This sequence is specific to the Eid prayers, in contrast to the Jumu'ah (Friday) prayer where the Khutba precedes the prayer.
Ibn Abbas's instruction and Ibn Zubair's implementation demonstrate this was the established practice from the time of the Prophet (ﷺ), ensuring the Ummah follows the authentic Sunnah in both the absence of the call to prayer and the correct order of ritual components.