CTA's forms submissions not tracked on outside site




I have a CTA on a blog managed by Hubspot. click on the CTA at the bottom of the page
I have an outside website which embed the hubspot tracking cookie.
I use contact API via forms to send new leads to Hubspot (I send the hubspot cookie by API)
I can see views and clicks through statistics but not the forms submissions...
Is it possible see them?
Thanks a lot,