Generally, yes, the legal action must conform with U.S. law. However, for that to happen, someone would need to object to what took place....this is why I stated in the earlier post that, "if you wanted to overturn the annulment" it would be possible to do so.
In other words, if nothing is done, the annulment would be considered legally sound. Conversely, if it were objected to, a court would examine the situation and make a determination as to whether it was handled in an appropriate, legally sound, manner. If it were not, then it would be set aside.
What it comes down to here is whether anyone is going to object. If the first wife objects, she would likely be able to set it aside. As you've alluded to, this is so because neither party was a resident of Mexico and therefore shouldn't have been entitled to obtain relief in that country.