Hi there,
That’s not an issue we’ve come across before, or had any users report.
Let’s see if it is related to one of the plugins installed or not on your site first. Please follow these instructions to install and enable the Health Check & Troubleshooting plugin so that both Gravity Forms and Gravity PDF are active and then replicate the issue and see if the conditional fields are still not showing up correctly when the PDF is created by the API.
If the PDF begins working by following the steps above, keep enabling plugins one by one and retesting until you find the problem.
If the above doesn’t yield any results, please use our support form to submit additional information about your environment.