You should learn more about the application's specifications, and can withdraw access quickly.
Instagram has relaxed the controls for some time on applications from third parties, and now you have more leverage in your hands. It adds more powerful data sharing controls that allow you to shut down a genius application quickly.
There is a new permission screen that clarifies the needs and preferences of a third-party user and new privacy controls (under Settings > Security > Apps and Websites). The new controls will take a while— in the next six months, they will hit phones.
This is probably a reaction to Instagram's behavior being closely examined. While most of the privacy problems surrounding Facebook's central service, Instagram has been experiencing problems with overreaching advertisers and abuse of data from third-party apps.
These enhanced measures will not necessarily help Instagram avoid another privacy fiasco, but they should remind you to be cautious and to remove old applications which could collect more information than you want.