The document is sent from Acrobat Pro to the recipients email using "Send for Signature". In the email there is a link to click to open the document and fill it out and sign at the bottom. Clicking that link opens up the recipients default web browser. I've sent several test documents to myself and opened the link using the following web browsers...
Firefox
Safari
Google Chrome
All have the same result. The tab sequence is out of order and not the way I have them numbered.
Like I said above, while adding text fields to my PDF document the order is correct. When I preview before sending the order is correct. However once the document is received the tab sequence is not in the correct order.
All of these browsers have an internal PDF viewer plugin which often doesn't work correctly, especially when it comes to form fields.
Try saving the file locally and then opening it directly in Reader/Acrobat. Does it work correctly then? If so, the problem is with the browser plugins.