What these do is make a new growth like you see. It will grow some big leaves from the growth, then a flower spike will emerge from amoungst the leaves. Towards the end of the flowers you will notice that the base of the new growth from which the spike is coming will fatten and a bulb will form beside the spike from the middle of the leaves.
Not all growths produce the flower spike, the plant needs to be big enough and healthy enough to do that.
As you have been told, if it's going to flower the flower spike will form from between the leaves of the growth BEFORE the p-bulb then forms in the same growth.
So what you have is a new lead growth that will certainly form a p-bulb, but could also produce a spike

---------- Post added at 04:58 PM ---------- Previous post was at 04:54 PM ----------
Orchids like Oncidiums also produce the flower spikes from amoungst the leaves of a growth, however they usually grow the spikes from the base of the bulb after the p-bulb has formed in the middle of growth's leaves.
The difference with Zygos is that the spike forms before the p-bulb rather than after. It forms in about the same place, but comes before the bulb forms rather than after.
I would cut away the spike part after flowering, I can see some in the picture, but leave the main part of the growths with their leaves and bulbs.
---------- Post added at 05:00 PM ---------- Previous post was at 04:58 PM ----------
Oh and they can flower more than once a year. Mine was really small and weak for several years, but has flowered twice in 12 months. Basically now it's healthy again each new growth, of which have each taken about 6 months to mature, has produced a spike before the p-bulb as described above.