I'm a novice too and had my phala rebloom when after its first flowering the stem stayed alive. I consulted the OB and web sites where the consensus seemed to suggest that reblooming had associated with it not quite the same quality of flower and that cutting off the stalk was preferable. I didn't follow the advice wanting to see what happened. I have 4 white blooms, not as many as the first flowering. Beside this phala we have another whose stem died off after the first flowering but it has developed new healthy leaves. The end of my story will be in the autumn when I see how well the newly leaving phala fares- I expect it to flower and alongside have the second flowering plant which will...?
Welcome to Orchid Board and great growing on the reblooming. It's always exciting when you get a rebloom, especially a 1st reboom. Your orchids look really happy.