I wouldn't consider them synonymous.
Upbeat
, other than the strictly musical definition of the last beat of the bar, is an expression of positive sentiment & is not exclusively used to describe music. e.g. this definition & these synonyms.
Up-tempo music
, on the other hand, describes a fast tempo. It may also imply positive mood (can't find the example i saw of this implication the i saw this week, damn!), but generally not. e.g. this definition
[added]
Now, as for your identity relation: i don't think that hold either. According to a quick bit of research that i did:
downtempo
& downbeat
refer to a style of ambient music;
downbeat
is the first beat of the bar (as you already observed), & by analogy it also applies to the beginning of a rehearsal or performance;
downbeat
is the opposite of upbeat
in the sense of meaning a negative mood as opposed to the positive upbeat mood.
So while upbeat
& downbeat
are opposites in terms of mood (positive/negative) & complements in terms of positions in the bar (last/first), uptempo
& downtempo
don't seem to have a similar relationship. Further, while the words downbeat
& downtempo
refer to a style of ambient electronica, they are not interchangeable in any other use.
In summary: upbeat
& uptempo
are not synonyms; downbeat
& downtempo
are both names for a style of music; upbeat mood
is the opposite of downbeat mood
; uptempo
& downtempo
aren't really antonyms as the former is a general description & the latter is a specific style.