Physical Interpretation of Field Operator in Quantum Field Theory and Mode Expansion

I’m struggling to understand the physical interpretation behind the field operators $ phi(mathbf x)$ and $phi ^dagger (mathbf x)$ in quantum field theory. My understanding is $ phi ^dagger (mathbf x)$ is an operator which creates a particle at a position $mathbf x$. p37 of Quantum Field Theory for the Gifted Amateur (Lancaster & Blundell, OUP) says that from this definition of $phi ^dagger (mathbf x)$, we can then write
$$ phi ^dagger (mathbf x) propto sum_{mathbf{p}} a_{mathbf p}^dagger e^{-i mathbf p cdot mathbf x}.$$
However this is different to the approach in Peskin & Schroeder. They write out the mode expansion for $phi(mathbf x)$ for the Klein-Gordon field (eqn 2.25) as
$$phi(mathbf x) propto int frac{1}{left ( |mathbf p|^2 + m^2 right )^{1/4}} left ( a_{mathbf p} e^{i mathbf p cdot mathbf x} + a_{mathbf p} ^dagger e^{-i mathbf p cdot mathbf x} right ) d^3 p.$$
I understand that we have two terms since we require $phi(mathbf x)$ to be Hermitian. However does this not contradict the definition that $phi^dagger (mathbf x)$ creates a particle at a position $mathbf x$ above? Is it correct to interpret $phi(mathbf x)$ as an operator that creates a particle at $mathbf x$, or is it better to just ignore the interpretation and only think about the results the theory gives from performing measurements?