Thanks to both of you. I missed a clear understanding of $Q_f \otimes \mathbb C\simeq Q_f^{\mathbb C}$. Indeed one should verify a few, trivial here but necessary, things: the map $\mathbb R\{x,y\}\otimes \mathbb C \rightarrow \mathbb C\{z,w\}$, $f\otimes \alpha \mapsto \alpha f^C$, 1) respects operations and convergence, 2) has a well defined inverse (since the ''formal real and imaginary part'' of a convergent complex series, put in $\mathbb R\{x,y\}$, converge), 3) commutes with the operation of "taking $i$-th derivative", so maps $I_{df} \otimes\mathbb C$ onto $I_{df^{\mathbb C}}$.

Thank you for your search anyway. It is unfortunate that a foundational and widely known paper like this has no translation, I'm still hoping there is some "unofficial" english version somewhere. Meanwhile, I'll sit down with a German vocabulary...