They searched the phone before obtaining a warrant. This ruling is troubling not because of the case at hand, but because of the precedent it sets. It's definitely an area where the law could be better defined.
Searches do not invariably require warrants. For instance, you will be searched "incident to arrest" if you are formally arrested (ie, not merely detained). This is part of why the police cannot casually arrest random people. Similarly, the police cannot casually impound random cars.
Is a warrant required to search a vehicle during an impoundment? During a routine traffic stop, a warrant, permission, or probable cause is required to search a vehicle. Doesn't this ruling set the precedent that if and only if the police would be legally allowed to search a vehicle, they may search a phone contained within that vehicle? (IANAL)
However, in South Dakota v. Opperman (http://supreme.justia.com/us/428/364/case.html) the court upheld that police may search and inventory a car without a warrant, even though the car was impounded for parking violations and not on suspicion of drug offenses (as it turned out was the case). I would conclude, therefore, that a car impounded during an arrest can definitely be searched.