Following a CiviCRM checksum link doesn't populate civicrm tokens but logging in populates the tokens.
I assume the "page" you're referring to is using a Webform, If that's the case, then you should mention that in the title.
The link to the form should be of the format http://example.com/your_form?cid={contact.contact_id}&amp;{contact.checksum}.
On the CiviCRM tab, in the Contact Field section, select Existing Contact, as well as all the fields you want to appear on your Webform.