Editor 

If quotas have been enabled for a storage, they will immediately take effect on most of the actions in the storage. Any upload, copy, create, cross-storage-move or replace action will be monitored and checked whether the result will result in exceeding the quota limits. If this happens, editors get a verbose error message.

Backend Integration and Warnings 

Warnings are issued as flash messages and shown in the FILE > Filelist module [1]:

Quota warning in the File List Backend module

Quota warning in the File List Backend module