Praise be to Allah.
I put this question to our Shaykh, ‘Abd ar-Rahmaan al-Barraak (may Allah preserve him).
Yes, he has to make it up, because fasting that day was obligatory for him, and he broke his fast because he had an excuse.
Likewise when he reaches a city where the people are not fasting, then he has to break the fast with them, because the ruling he should follow in that case is the ruling of the people of the city to which he travelled.
But if he set out travelling before Fajr, then he does not have to do anything, because the ruling on fasting before dawn breaks does not apply to him.
And Allah knows best.