The replacement of tags, in your case {name:value} & {email:value}, does not occur until after the Form has been submitted.
At the point of clicking on a Field in the Form the tags are just a string characters as you see them and that is what gets passed to the new window.
If you want the values in the fields to be passed at the click of a field/button then you will need include some Javascript in the Forms Properties tab that extracts the values from the fields and opens the new sign up page. Your onclick would then look something like
onclick="mysignup()"
And in your Javascript you would have something like (provided as is, not tested)
function mysignup(){
var name = document.getElementById('name_field').value;
var email = document.getElementById('email_field').value;
window.open('http://url.com/signup/' + name + '/' + email);
}
If the external sign up page doesn't require a users intervention then you may be able to do the sign up as part of the PHP post submission scripts if the external site provides the capability. There are some examples of this on the RS Form forum.