Receiving email through both Fastmail and Gmail?

I have a Google account. I use it to host my personal domain and to store documents. A year ago I also purchased a Fastmail account so I could have secure email.
The Fastmail team helped me point my mail servers to Fastmail. Now I use the ios Fastmail app to check my email. But I also see my email in the gmail app. Is this how it’s supposed to work?

I moved my email from Google to Fastmail and I don’t see any new email on the gmail side since I moved my mx records.

Thanks for the response. I put in a ticket to Fastmail support. They said they checked and say things on their end are set up correctly. They advised me to contact Google Support. Good luck with that.