It's not attempted murder in the United States, but it could rise to a full murder charge depending on what the prosecution is willing to charge. This gets tricky as murder in the United States is usually defined as "unjustified homicide" (as it is in the other countries) but it also looks at the circumstances. Smith shot Jones in the face after the poison was administered. Whether Smith delivered the fatal blow to Jones or not does not actually matter, as Smith intended to kill Jones and certainly wouldn't have helped Jones to live had he known about the poison.
Another argument is that Smith unlawfully entered Jones' home, which is a felony, and thus the Felony Murder rule might apply.
The likely scenario is that Smith might get offered a plea deal for Attempted Murder charges and the prosection won't take the case before a jury. However, if Smith refuses, the prosecution can try him for both Murder and Attempted Murder (since you can charge lesser and included sentances but not convict for lesser and include, which means the Jury can hear the whole case and decide if he's guilty of "First Degree Murder," and if the answer is no, can try "Second Degree Murder" then "Attempted Murder," "Manslaughter," and finally "Improper disposal of a Body" or related charges) and let the jury sort it out. They have Smith Dead to Rights on Breaking and Entering, and any charges related to improper disposal of a body or failure to notify authirities, so he has some jail time to look forward too.
As a general rule, the fact that the guy was already dead wouldn't matter because the autopsy rarely can determin how accurate the time line was when two traumatic events occured. Suppose Jones was not dead at the time Smith shot him, but was pretty darn close. One could argue for murder because shooting someone in the face is generally not advised as treatment for poison... or any fatal injury for that matter. Thus, there was a slim chance that Jones could have survived long enough that he coudl be rushed to the hospital and survived OR even that the poison wasn't used in enough quantitity to kill him... but never the less, it was going to cause injury. But for Smith shooting the man, Jones might have survived.