Yes, that reference to the future is what makes it refer to a completed future action. If we had no future reference we would think it is referring to the past. For example:
Espero que hayan empezado a construir la nueva urbanización antes de septiembre.
(referring to the future)
Espero que hayan empezado a construir la nueva urbanización.
(referring to the past- unless it is omitting the future reference because it is assumed, i.e. it was mentioned before in the conversation so there is no need to repeat.)
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