I don't know. Felix and his wife were married in Moneymore, County Londonderry and their first few children were born in that area. But Felix himself was born in Ardboe, County Tyrone. I don't know if that has any bearing on where he would be sent.
The rules were that you were charged to the parish where you had 'settlement'.
You acquire 'settlement' by being born there, or by marrying a man who had 'settlement' there, or by living long enough in that parish. Initially you had to be there for 5 years, and latterly it was reduced to 3 but I forget exactly when.
If Felix lived long enough in Ardboe to acquire 'settlement' there in the eyes of the Glasgow parochial board, and his children were born in Ardboe, I would expect the Glasgow parochial board to have contacted the authorities there, told them that one of their parishioners had applied for relief and asked them to pay for whatever it cost them to deal with Felix's family. The authorities in Ardboe, instead of sending money to Glasgow, might have instructed the Glasgow parochial board to send the family to Ardboe, probably to the poorhouse or workhouse serving (but not necessarily in) Ardboe, because that might be cheaper.
Or they might have sent Felix to Moneymore and the children to Ardboe. It wasn't uncommon to separate families so there is no guarantee that they were all sent to the same place.
I am a little surprised if the Glasgow parochial board records apparently don't say where Felix and children had 'settlement'. This was a fundamental element of the system, because it enabled a parish to avoid bearing the cost of people from other parishes, or at least to claim reimbursement. So it was always one of the first details to be collected by the parochial board when someone applied for relief.