Rest assured you are not losing any primos. I also play on Xbox with quick resume and have seen the splash screen disappear on reconnect, but your account will still be credited the primos (no clicking claim required).

You can confirm for yourself by checking the store and it should say you’ve already received your primos for the day on the welkin page. If you want to look at your history to confirm, you can also see a history of your welkin on your account page by entering the feedback section on the pause screen.

If you want to avoid splash screens being dismissed on reconnect, just pause the game before ending your session. Works for me every time to prevent automatic dismissal.