Yes, Dzhokhar Tsarnaev Has Miranda Protections
This is relatively simple. The FBI may not “Mirandize” Dzhokhar Tsarnaev when they interrogate him. As a result of this, anything he says during that interview that doesn’t relate to immediate threats to the public (like other bombs) would not be admissable as evidence against him in a trial. This is something that the FBI and the prosecutors have to weigh, to consider the need for public safety vs. the need to prosecute him. As the prosecution should be iron-clad anyway, I don’t think they ever need to Mirandize him as they never intend to use his statements against him in a court of law.
We have the right not to incriminate ourselves. We don’t have the right not to be tricked into telling the cops where a large cache of explosives is, if that admission is not used to prosecute us.
Furthermore: The public safety exemption means that things that are revealed without being Mirandized which are direct threats to public safety can be used against you in a court of law. So, if you reveal where the bomb that you have strapped to a bridge is, that admission can be used against you. What the legal logic of that is, I don’t really know, but I guess it’s that the cops have no realistic way to get that information in a timely fashion, and they can’t say, “Just tell us where they are and we won’t use it against you.”