Pesticide use in organic farming

I am a regular visitor to farmers market at the cricket grounds. I like to buy from there as I believe the produce sold there are organic. But, as I understand it, even the certified organic products worldwide are allowed to use a certain percentage of pesticides, etc. I would like to know which pesticides or other chemicals are used by local farmers, and how much quantity. Especially I would like to know this information of the big farmers in Cayman. As there is no government control in Cayman about calling a produce organic, I am wondering whether the farmers use them liberally and still call is organic, only because they grow it.

Read Auntie’s answer and comment on CNS Local Life