Translation:Last month, the synagogue was under construction.
yes.. but with "le mois dernier" we know there is a duration so we use "l'imparfait". The "passé-composé" is if the action was short/small (?) in the past and it is finished. With the "imparfait" may be synagogue is still (?) under construction, with the "passé-composé" the works are finished. I hope I help you.