The comparison isn't actually between "composed of" and "composed with", it's between "composed of" and "composed". In brief, "with us in mind" is a separate adverbial phrase that is not attached directly to "composed".
To illustrate, these are correct sentences:
- "With that in mind, I composed the essay."
- "I composed the essay with him in mind."
- "This is the essay, which I composed with him in mind."
- "With that in mind, I wrote the essay."
There are two meanings of the word "compose" that are relevant here. Meaning 1 is "to create or craft (a work of art or writing)", which is the meaning in the phrase "composed with us in mind". Meaning 2 is "to make up or constitute", which is the meaning in the phrase "composed of".