I would add that while "I have to" and "I need to" aren't synonyms, they are very often used interchangeably and are generally understood to have more or less the same meaning in English.
That said, we are learning Czech here, and "musel jste" does not translate from Czech to English as "did you need to." Tip: I find it best to stick as closely as possible to the original, unless doing so results in a really strange translation... which can certainly happen! :-)
Let' not just open a dictionary and take any listed translation as an equivalent. I have seen way too many horrible, even completely absurd, translations, where the wrong equivalent was picked from the list.
When I am translating to or from English and I am unsure, taking a Czech to English dictionary is not enough I have to take a dictionary with good explanations and examples of usage such as Merriem-Webster or similar.
In this case case there is some overlap of these two words (muset and potřebovat, must and need), but they are not identical. I suppose the difference between them will be very similar in both languages.
This is a Good News/Bad News situation. "You had to work" is an accepted translation. Good News: Duo did what it's supposed to do by automatically accepting contractions: you had > you'd. Bad News: In this case, the auto-recognition is very strange and I don't think you'd hear it, at least not in the US.