Tycondrius mulled over the situation in his head as he dragged Willow out of vision and earshot-- far from Iyuri's Gold-Rank senses.
If the girl had chosen to join the crew of Neptune's Revenge, he would have accepted her as being indirectly part of his faction.
As she refused... he needed to understand just where her loyalties lied.
He would make a few inquiries of the child. Based on her probable answers, it was very likely that he would kill her.
After he did so, it would be optimal to kill her brother as a precautionary measure.
...Unfortunately, it was unlikely he would.
Tycon prioritized influencing Princess Iyuri positively. If he was questioned for killing Willow, he could grant a simple explanation.
The enemies of Sol Invictus had but a single fate.