Feeding & Playtime - what am I doing wrong?

We have a 10.5 week old lab & I’ve been following a daily puppy routine from a dog trainer - she recommends play & exercise AFTER food which had been working ok but now that our pup is slowly starting to want to burn more energy, I’ve been second guessing this.

After I fed him this morning, I took him out to our garden to play a little fetch (about 5-10 mins) & about 20 mins later, he retreated to his crate & threw up some of his breakfast - I felt absolutely horrible :( I started researching online & I’m starting to see many conflicting opinions with feeding times around exercise..

Does anyone have any recommendations on what to do here? What does/did your puppy routine look like around this age?

Any help appreciated.. thank you!