I am a career prosecutor. The issue is complex. In general, the 4th Amendment to the US Constitution prohibits unreasonable searches and seizures of property without a search warrant. A search warrant is issued by a judge who is presented with information, under oath, by police officers, as to the reasons why they believe that the item, building, vehicle, or other container may contain evidence of a crime. The standard is whether or not there is probable cause to believe that the place sought to be searched has that kind of evidence of a crime.
The 4th amendment right to be free from unreasonable searches and seizures without a search warrant approved by a Judge, actually has many exceptions that have developed over the years. It is the study of more than two years in law school, studying criminal law and constitutional law to know all of them. But the issue in this case was this: When a person is arrested for a criminal offense, anything on their person, in their vehicle or within their reach, can be seized and searched by the police. For instance, when a person is arrested in their vehicle, the inside of the vehicle, except for the parts of the vehicle that are separate (trunk, etc), can be searched and examined. Also there is an exception for what is called exigent circumstances. For example, you stop someone who is suspected for having kidnapped someone. You may be able to search the trunk for that person, without a warrant, to ensure their safety. You just may have to justify that decision later if the search turns up incriminating evidence.
The issue in the Supreme Court case is not whether the phone could be seized. Based on the arrest, the seizure was all right. The issue is whether, once having seized the phone, you could go into that phone and peruse the information inside, without a search warrant.
An exigent circumstance that might allow you to do that at the scene of the arrest is when you have reason to believe that the phone might hold information that would lead to the location of a kidnapped child. Absent that kind of situation, the case merely states that, if you want to go into the phone that has been seized, and indeed, into any device that has information in it (laptops etc) you need a warrant.
Already prosecutors around the country are setting up procedures for quick search warrants regarding these situation. It has always been true that prosecutors and Judges can be on call to respond any time of the day or night, to address those issues. Indeed, the court recognized that these warrants, if there is probable cause for them, can be quickly obtained.
None of this is new. It is just new as to cell phones.