That probably comes across as a bit abrupt.
p125 says "Each Combat Round begins with the participant (Adventurer, adversary or monster) with the highest initiative acting first, spending one of his Combat Actions. This is followed by whoever
has the next highest initiative and so forth until the participant with the lowest initiative has
acted. Then, if anyone still has any Combat Actions remaining, the cycle repeats until all
available Combat Actions for all available participants have been spent."
and
"Initiative is measured in Strike Ranks and rolled at the start of a fight, remaining in play unless something occurs to force Initiative to be re-rolled. This is up to the Games Master to decide but at the very minimum an Initiative roll lasts for an entire Combat Round."
So you can re-roll initiative when a new combatant joins the combat if you as GM decide that it is something that forces Initiative to be re-rolled. In either case a new Initiative roll is only made at the start of a round.