"Tuesday is not my day."
Translation:Wtorek to nie mój dzień.
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After "jest" you would need Instrumental ("Wtorek jest nie moim dniem"), but that would be like "Tuesday is not my day but someone else's"). In general the negation should be before "jest" (you negate 'being X', not just 'X').
The most natural answer to me is "Wtorek to nie mój dzień" or "Wtorek to nie jest mój dzień" (This is actually not the 'jest' construction because it has 'to'), alternatively "Wtorek nie jest moim dniem".
Maybe I'm mixing things here. So do we use genitive on negative sentences only when the affirmative is accusative?
Yes, if you read somewhere here (it may be even in my own older comments) that "Negation = Genitive", that's way too simplified. Only negated Accusative turns into Genitive, other cases stay unchanged.
Moreover, that only happens if Accusative was needed by the verb. Sometimes it's needed by the preposition and then negation changes nothing. Although I guess we could say that it's simply not the preposition that is negated, so we shouldn't expect a change in cases.