Hola Cachoot

In the lesson we explain that primero becomes primer when it's placed in front of a masculine singular noun, so, as in this case the noun is "marido" (husband), a singular masculine noun, if you say he is not your "first husband" you need "Carlos no es mi primer marido" (not mi primero marido). If you were talking about a first wife, for example, "primer" wouldn't apply because now it'd be a singular feminine noun: mujer, so:  Carlota no es mi primera mujer (not primer mujer)

But here's a more specific lesson on primer and tercer where you can see more examples.

I hope this clarified it.

Saludos