*I may be wrong, but I believe this is just a common grammatical construction in Italian.
Cond. + che + Imp. subj.
Basically, when the conditional requires a subj. clause, it requires the imp. subj. not the present subj.. So while Ind. goes "Voglio che mi chiami", the conditional mood requires. "Vorrei che mi chiamasse". I think this construction is called the "periodo ipotetico" - https://ciaoitaliablog.wordpress.com/classes/hypothetical-phrases/
English grammar has a similar construction.
I suggest (Ind.) that you be (pres. subj.) early
Contrast that with,
I would be (cond.) happy, if I were (past subj.) rich.
I would be happy, if he were to call me.
I can only think it's because the correct translation would be 'I would like him to have called me' but Duolingo seems to regard this as incorrect. (There are some more, similar, examples in this section) I'm going to assume that's the case in reality but remember to enter Duolingo's preference in order not to get marked wrong!
nwws: the verb form is subjunctive imperfect, but it's meaning is present tense as translated. For example in English you can say "I would him to call me (now) or "I would like it if he WERE to call me now." Looks like past time's being referred to but it's really present time.