The timezone shown on your invite page depends on whether you've created your link with the Displayed Timezone option set to Invitee Local Timezone (the default setting) or Locked Timezone.
zcal will automatically detect your invitee's timezone and adjust the display of your available times accordingly. If the invitee prefers to view your availability in a different time zone, he can change the timezone using the timezone dropdown.
If you're meeting in person, selecting Locked Timezone will ensure that everyone sees your availability in the same timezone as the one set in your link settings (this should be set to the timezone at your meeting location). Links with this option will always present availability in the same timezone, regardless of where in the world your invitees are.