"If I understand you correctly, you need me."
Translation:Jestli vás dobře chápu, potřebujete mne.
This is not a good word order, vás should in the second position or, when stressed, the last word.
"Jestli vás dobře chápu, mne potřebujete." is not accepted. Because mne should come in second position?
Mne can also come in the first position, but it sounds strange here in the compound sentence, it would have to be stronly stressed when pronouncing.
Sadly, I can't point to any easy rule to apply. Maybe someone else will be able.
Moving the pronoun to the front means that it is being fronted as a result of pre-existing context, as if we just finished discussing someone else, whom the other party does not need or otherwise has a relationship contrasting with their need of us. The other possibility is that we are not so much fronting the pronoun as placing the verb to the final focus position. Maybe they need us but want her.
We probably have to accept you order because to express this in English, we might stress need me jointly or just the need.
"Jestli tě dobře chápu, potřebuješ mne." is accepted. If your translation was not accepted you should report it exactly including the diacritics. If you can't do that, you should use "My answer should have been accepted" - actually, that is the preferred way of reporting missing translations, but you are always welcome to ask questions.