It doesn't, no. Wild pokémon that become terastallized go on about their days quite normally- the high aggression is only clear if someone gets too close to them. Only another terastallized pokémon is capable of shattering that crystal surrounding one.

This shattering can stun a pokémon of course, but otherwise doesn't harm them.

[It was deeply looked into, just how it affected and effected a pokémon, along with how best to harness the phenomenon so that they could use it. Turo had managed something remarkable in the design of the Tera Orb as well.]