Vicky is right.
However, in our last meeting they agreed to revisit this rule to cover precisely the situation you have described. I don't think a strictly literal, one-dimensional interpretation of the words "at the same time" is reasonable because sometimes the Brit has to stay behind and close down the household.
They have already begun rewording the guidance on this
For the nonce, you don't have to wait before applying if your spouse intends to settle with you.
If the British half is already in the UK when the non-Brit arrives, that's fine.