Catalyzes the transfer of adenosine 5'-monophosphate (AMP) to Tyr residues of target mitochondrial proteins (AMPylation). Involved in redox homeostasis by regulating the cellular response to oxidative stress. Regulates protein S-glutathionylation levels possibly by AMPylation of deglutathionylation enzymes such as glutaredoxins. ATP + L-tyrosyl-[protein] = diphosphate + O-(5'-adenylyl)-L-tyrosyl-[protein] Forms probably one or more intrachain disulfide bridges. Belongs to the SELO family.