The Mishnah (Shekalim 1:1) teaches that on the first of Adar the courts of each city would announce to their inhabitants and the villages surrounding them that the time has come to bring their contribution of coins to the Temple.
The Talmud Yerushalmi explains that the reason Adar and not a different month was chosen is that the first of Nissan was the day designated for Terumath Halishkah. The Rabbis found that it was necessary to begin announcements already in Adar for people to get their contributions in on time.
Although not mentioned in the Mishnah, we also start reading the pericope of Mahasith Shekalim on the first of Adar which is the same day that we announce the coins. However, they differ on the reason each is performed respectively.
ר’ לוי בשם ר’ שמעון בן לקיש צפה הקב”ה שהמן הרשע עתיד לשקול כספו על ישראל אמר מוטב שיקדים כספן של בני לכספו של אותו הרשע לפיכך מקדימין וקורין בפרשת שקלים (תענית א:ה ז,ב)
Rabbi Shimon ben Lakish in the Talmud Yerushalmi teaches us that God decreed that “the coins of My Children should precede those of that Wicked Man (=Haman).” In other words, we read the pericope of Mahasith HaShekal on the first of Adar so that it precedes the reading of the Meghillah (starting with the thirteenth of Adar) which tells of the coins of Haman. God had the foreknowledge that in the future Haman will take the money of the Jews and present it to Achasuerus to get permission to destroy them. (Esther 3:19)
How do we understand the reason for precedence? Rava (Bavli, Meghillah 13b) gives us some insight. The Jewish People in the story of Purim (coins of Haman) were saved because of the merit of their contribution of coins to the Temple when it was still standing. God instituted the reading of the contribution of coins at a calendrical date earlier than Haman’s coins as symbolic of this.
אחר שברא הקודש ברוך הוא רפואה למכה. דאמר ריש לקיש: אין הקודש ברוך הוא מכה את ישראל אלא אם כן בורא להם רפואה תחילה
In contrast to the Talmud Yerushalmi, Rabbi Shimon ben Lakish in the Talmud Bavli considers not the early reading but the early announcement (Meghillah, 13b) to serve the purpose of creating a symbolism:
אמר ריש לקיש גלוי וידוע לפני מי שאמר והיה העולם שעתיד המן לשקול שקלים על ישראל לפיכך הקדים שקליהן לשקליו והיינו דתנן באחד באדר משמיעין על השקלים ועל הכלאים
Elsewhere, the Talmud Bavli (Meghillah, 29a) states contrarily that it is the announcement that serves the purpose of creating a symbolism:
וכיון דבניסן בעי אקרובי מתרומה חדשה קדמינן וקרינן באחד באדר כי היכי דליתו שקלים למקדש