In this case, "que" introduces a subordinated clause, so it doesn't have to be a specific verb tense. It depends on what you want to say. "que ela coma (pres. subj)" = "that she would eat" ; "que ela comerá (fut. ind)" = "that she will eat"; "que ela comeu (pret. perf. ind)" = "that she ate", etc.
the first time I saw this I translated "supor" as "guess"- it accepted it. In another sentence I used "guess" and it was marked wrong and "supor" was translated as "think". When I got this sentence again I used "think" and it was marked wrong. Is it context?
Supor= suppose, assume, guess, think?