How does the domain and certificate work in case if customer purchases my app from aws marketplace ( ALB routed over https)

When a customer purchases and deploys your application from AWS Marketplace, there are a couple different ways the networking and SSL certificate can be handled:

1. Bring your own domain and certificate - In this model, the customer would purchase a domain name and SSL certificate separately from a domain registrar and certificate authority. The ALB in their account would be configured to use this custom domain and SSL certificate.
2. Use an AWS provided domain - AWS provides a unique subdomain for each Marketplace deployment under the subdomain prefix "awsmp-XXXXXXXX.marketplace.awsapps.com". An ACM certificate is automatically provisioned for this subdomain. The ALB would use this generated domain and cert.
3. Vendor provided domain and certificate - As the ISV, you could purchase a wildcard domain (e.g. *.myapp.com) and wildcard certificate to cover deployments. Each deployment would receive a unique subdomain you configure on the ALB.

Option 1 gives the most flexibility and control to the customer. Option 2 is the simplest since AWS handles the domain and certificate automatically. Option 3 allows you as the vendor to manage domains and certs centrally.

When listing your product in AWS Marketplace, you can specify which options you want to support for purchasing customers. This allows them to choose the custom domain or AWS provided domain flow at deployment time.

Hello.
I believe that the purchaser of the application in the marketplace would need to prepare the domain and SSL certificate.
The application exhibitor would only be able to provide up to a container image.
https://docs.aws.amazon.com/marketplace/latest/userguide/container-product-getting-started.html