They just pop out on short spikes. I looked around for a photo of one of my Cochleanthes that shows the habit and couldn't find one (all are flower closeups) but found a Bifrenaria and a Bollea that are in the same group, with the same flower habit. (probably have been reclassified anyway). I included the Cochleantes just for comparison though they don't show the "origin of the spikes that well Here are links:
http://orchidcentral.org/Images/Zygo...%20inodora.jpg
http://orchidcentral.org/Images/Zygo...dorana%202.jpg
http://orchidcentral.org/Images/Zygo...dorana%202.jpg
http://orchidcentral.org/Images/Zygo...wailesiana.jpg
http://orchidcentral.org/Images/Zygo...20discolor.jpg