Completing primary missions increases notoriety, which triggers hints for the Sheriff.
Sheriffs can check mailboxes to receive hints about the Outlaw's last known location or completed tasks. West Hunt on the web
Outlaws can perform "innocent" side missions to lower their notoriety and blend in better, though this consumes valuable time. Completing primary missions increases notoriety
Outlaws can use special skills like teleportation or shapeshifting to evade detection. West Hunt on the web