Technically, I think this is Bridgeport tapping and not drill press tapping, but you'll understand what I mean when you see the video.
This is something we do on a regular basis these days. Back before Teranews stopped allowing me to access this group (now fixed), I was posting about how we were hoping to develop this and asking lots of questions.
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Truth is, this customer had problems blowing up their Tapmatic tapping head in this set-up and this is the video showing how the perform the process. Our guess is the end user is doing it properly for this video but might have been using a different "technique" of pulling that feed arm or even using power feed when not on camera...