Publishing issue

while the domain is still being transferred, the site I published is not up but rather in its place, an old site someone did. Will my site replace this or must I do something other than publish the site? In regular html, I would upload to the server and htmls would be over-written

To make your site live, you must make it public and connect the domain to your site. 

Yes but I transferred it to squarespace so should it not just connect? There's no other instruction other than connect it or transfer it, if I understand

In that case, you should probably reach out to Customer Care for help.