When a person signs a form, signature shows up on my original PDF with a blue timestamp. How do I prevent this from happening?

If you're referring to this annotation that is being added to signature in original PDF shown below, then there is no option to turn off this timestamp. It gets automatically generated and added upon submission.

However, I've successfully escalated this as a feature request to our developers. Also, please note that we can not provide you with when or if this will be implemented. If there is any update, we will inform you via this support ticket.   

I hope I have been of any help.

Should you have any further inquiries, we will be more than happy to help.