You'd be absolutely right if the rule said "beginning of the close combat phase
." As far as I can tell each individual combat
is considered a "round" although it is poorly defined in the book.
For example; "pursuit into a new enemy"
"If this enemy unit was already engaged in close combat, and that fight has not been resolved for this turn, then the pursuing unit will get to fight another round
of close combat!"
That's my take on it anyway.
I haven't scoured the rulebook to see if round is used synonymously with phase, but I don't think it is.
There is no rule in the BRB, or an FAQ of the BRB that says that "the player whose turn it is decides the order"
I'm not sure I'm misunderstanding you, but you know about the "Sequencing" rule in the box on page 10, right?