Tea extract contains in its composition tannins, flavonoids. They play the role of reducing ions and stabilizing of nanoparticle. See our article on the synthesis of nanoparticles of silver and gold with tea and rutin.
Most of the cases the nanoparticles are reduced by reducing agents. In the case of plants the reducing agents are may be secondary metabolites/NAD/proteins or if any. These reducing agents reduce Ag+ ionic state into Ag0 state and at the same time which stabilize and capping those nanoparticles. All these things are know by FTIR studies. That's why we call it as green/biosynthesis, here no need of any chemical reducing agents.
See also the use of aloe vera as a morphological modifier for the synthesis of precipitated calcium carbonate. Aloe vera provided some amino groups and its shrinking features to reduce size....