The district court judge, as reported in this news story has held that there was probable cause to arrest Daniel Robbins in this case, and that his rights were not violated. If this ruling stands, officers acted legally, although they might still be required to return the phone with the images.
Whether there is probable cause for an arrest (or a search) is always a very fact-based issue. I have not found the judge's actual decision, only a news summary of it, which can often be misleading. Specific facts about exactly what Robbins did or said may be important in determining whether there was in fact probable cause.
It appears that Robbins intends to appeal this decision. If he does there may be an opinion from a Circuit Court of Appeals expanding on whether there was probable cause or any violation of rights, and why.
Previous cases have established that normally there is no reasonable expectation of privacy for acts performed in public; that one my photograph or video record such public acts legally from anywhere that one may legally be; that there is a right photograph or record police officers engaged in official actions or the use of police powers; and that laws attempting to forbid such recording are unconstitutional when so applied. However, it seems from the news story that here the police officers were off-duty and not engaging in any official acts or use of police powers. That might change the ruling.
I rather expect the district court's decision to be overturned, but there is no case exact;ly on point that i know of, and one can never be absolutely sure what a court will do in a particular case. I can see why police officers may have felt threatened, and why the Judge may have been inclined to sympathize with them, although I think the decision was incorrect. But a Judge of the Appeals Court might possibly feel the same way. Until the Appeals Court rules, one cannot be sure what the law in this matter will finally be. (It is possibly, but statistically a bit unlikely, there there will eventually be a ruling from the US Supreme Court on this case.)
This article from Nolo Press discusses the issue of recording police, primarily in the context of police who are performing their official duties. It says:
Almost every court to consider the issue has determined that the First Amendment gives you the right to record (pictures, video, and audio) police officers in public while they are performing their duties. But that doesn’t mean you’re allowed to record if you’re doing so surreptitiously (secretly), interfering with the officer, or otherwise breaking the law.
The courts' primary rationale for allowing police officer recording is that the First Amendment includes the right to freely discuss our government, and the right of freedom of the press and public access to information. Given the prevalence of personal filming devices, more and more “news” is being gathered and disseminated by members of the public. The courts have found that freedom of the press applies to citizen journalists and documentarians just as it does to formal members of the press. (See, for example, Glik v. Cunniffe, 655 F.3d 78 (1st Cir. 2011).)
The Nolo article goes on to discuss whether a Section 1983 Federal suit against police officers who arrest someone recording their actions will succeed, indicating that this will depend on the specific facts of the case.
The Nolo article mentions that one is not allowed to interfere with an officer during process of recording. What exactly constitutes "interference" is not fully clear, and will depend on the facts of a specific case. The Nolo article mentions other circumstances when recording an officer may not be legal.