I agree with both - this is a very complex topic, as 은/는 and 이/가 have no clear-cut rules and are high contextual. Just learn through example, exposure, and practice.

"내일은 저는 일해요" 은/는 is supposed to mark the topic, which is what the sentence is about - often but not always the subject. The topic may be the object or even an adverb in the sentence. For example, consider "As for that problem, I couldn't solve it" (object) and "Joyfully is how we did it" (adverb). A topic just means the specific part of the sentence that is receiving the most attention. Sometimes, as in your example, two 은/는's may be used, which means the speaker is emphasizing two parts of the sentence. One of them is likely (but not 100 % guaranteed) to be the subject of the sentence, which is usually clear from the structure and context of the sentence. You need to understand some basics: 1) in Korean, the subject of a sentence may frequently be omitted. 2) if there's one 은/는, it often indicates the subject but not always. Sometimes the 은/는 may indicate the object or an adverbial part, while the subject has been omitted. 3) Another subject marker 이/가, if present, always marks the subject. But its use is more special. Examples: 1) 너무 좋다 (I like it so much) / 아 지루하다 (Ah, I am bored) - no subject, "I" is implied. 2a) 나는 행복하다 (I am happy) / 세계는 넓다 (The world is vast) - 은/는 marks the subject. 2b) 오늘은 일 안 해요 (We don't work TODAY) / 그 문제는 못 풀었다 (I couldn't solve THAT PROBLEM) - 은/는 marks the topic. An adverb(오늘) or the object (문제) is pulled to the front and marked with 은 to emphasize it. The implied subject is "나는". 3) 바람이 분다 (The wind blows) / 내가 그 일을 해야 했다 (I had to do that task) - 이/가 marks the subject. This is a rather deep and complex subject. You should read more details on grammar sites and practice with lots of usage examples to understand it.

I think you yourself explained exactly what you wanted to know about. The other way we say that is '내일은 저 일해요' '내일 저는 일해요' '내일 저 일해요'. It is up to the question or the intention of the person who answers. I suggest you consider the context or situation of the dialogue.