I remember having that done one too, so I looked into it more. There are two types of "tonometry machines", non-contact and contact. The contact tonometers indent your cornea to make measurements (after your eye has been given anesthetic drops). The non-contact "air puff" machines are more common, but apparently not as accurate.

So people who are inclined to avoid direct instrument-to-eye contact can request the "air puff" method.