The Vilna Gaon writes that the verse’s account of the Jews “doing what Mordechai wrote” refers to their giving charity and gifts.
Malbim explains that those Jews residing in the walled cities did not start to celebrate on their own, but only began when Mordechai’s decree went out.
M’nos HaLevi notes again that by writing it down, Mordechai retroactively transformed the Jews’ voluntary actions into the obligatory mitzvos of Purim.
R’ Dovid Feinstein adds that although the celebrations of Purim started on the Jews’ initiative, they submitted to the rule (and changes) of the sages.
The Dena Pishra writes that, at first, the Jews were upset with Mordechai for not bowing down to Haman (Esther 3:2), but now they recognized the wisdom behind Mordechai’s actions.
R’ Dovid Moshe Valle also points out that the Jews realized now that Mordechai had Ruach HaKodesh because he was able to summarize the events they witnessed into this multi-level text we have before us.