There are several synonyms for the phrase "were incumbent upon" that can be used to convey the same meaning. Some alternatives include "were required of", "were necessary for", "were obligatory for", "were essential to", "were mandatory for", and "were vital for". These terms imply that there was an expectation or responsibility for someone to undertake a particular action or task. Using different synonyms can help to diversify the language used in writing or conversation, and can help to convey the same message in a more vibrant or engaging way.