i suppose here you are referring to the 'low temperature indicator'. it comes on when the engine is cold. when the engine is heated it turns off. Nothing is wrong with your FIT.you can have a look at the user manual,
https://techinfo.honda.com/rjanisis/pubs/om/ATK620/ATK62009OMA.pdf
go to page 59. you can find all the indicators there. hope this helps