ROE change with the 'operation'. Different ops/areas have different ROE. Sometimes a 'visual' is required, particularly for policing operations, but that's not always the case either.
In some regions, the use of AWACs and other high value assets can ascertain the 'hostility' of the target aircraft (they know when he gets airborne and watch him). Do not confuse ROE with the status of the target either ... Most ROE will define what constitutes a hostile act and therefore whether the aircraft is hostile or not. Even then, engagement is unlikely without permission from the ground based Regional Commander.
Even being 'visual' (I say 'visual' as a purely grammatical statement - there is another codeword for being visual with a hostile aircraft) with a hostile aircraft does not necessarily give the fighter carte blanche to engage.