Why do I not need "se" here: Ti muži čekají na Kateřinu.
While in this sentence (of the same lesson) I need it here: Ti lide se divaji na stromy.
Those sentences are the same grammatically!
Čekat is not a reflexive verb; it does not have "se" or "si" as part of it. Dívat se, however, is reflexive. But the sentences you mention are somewhat similar in that both use na before the object of the waiting or watching.
Já jsem napsal: Tito muži čekají na Kateřinu. V čem je problém?
"tito" = 'these'
"Já ček_á_m" but "Oni ček_a_jí". "Já dív_á_m" but "Oni dív_a_jí". Do the accents "á" disapper because of "jí"?