Those are roots unfortunately! (though roots are always good as well). Spikes almost always come out from the side of the plant, in the 'crotch' of a leaf.
Just as a side note, I'm assuming your plant is Phal tetraspis, the species, in which case tetraspis should be written with a lowercase 't' and not uppercase. Uppercase is to denote a hybrid. (and as to the spelling, there's no 's' after the 'p'!)
__________________ Camille
Completely orchid obsessed and loving every minute of it....
This is my other tetraspis that's in spike and it is right next to a root, so who knows. I guess I'm still hopeful. This one has two spikes, there's another one on the lower side of the photo. Spike, root, root, spike.