No, placing brackets around chords is not required. You would generally only need to do that if you want to position your chords above the lyrics, ChordPro style.
Chords are auto-detected otherwise, but A and Am are tricky because they could be words or chords. Currently the app considers them chords if they are followed on the same line by other chords. You've found a gap in this logic by placing a chord immediately after the initial word A. I'll have to do some more work to support that situation. (Other text like "A spaceman [Em]came [G]traveling" would work fine.)
As a temporary workaround, you could change the initial A to lowercase and then it won't be transposed.