Balloon category licensing issues – BFCL – Applicable exemptions from recent experience requirements for BFCL licenses apply automatically?

They do not apply automatically. 
All licence holders issued in accordance with Part BFCL who avail themselves of the extensions set out in point (a) of provision Fifth of the EASA Resolution of 5.5.2020 regarding recent experience requirements will have received, prior to resuming the activity, a briefing given by an instructor with the appropriate powers of instruction, in which the theoretical knowledge necessary to operate the aircraft in question safely and to carry out the applicable maneuvers and procedures are refreshed. This briefing shall include abnormal and emergency procedures specific to the aircraft category, aircraft class or type and the applicable specific privileges.