You keep saying deficit. Do you mean the trade deficit or the governmental deficit?
[edit later after parent edit]
Ok I think you are saying governmental spending deficit. And your link doesn’t go nearly so far as to say that you must account for every governments spending in the EU to account for this.
Do you have any other links? This is a much more expansive view on the relationship between deficits and inflation than I’ve read before.
It's like a deficit in Kansas does not result in inflation in the US, because Kansas does not have its own currency.