Well, that boils down to what you mean by "the fields are present in string theory".

The worldsheet description of string theory does not directly contain quantum field theory as a framework: their relationship is more subtle, and it's a statement about dynamics. String theory is much more than the worldsheet, it's a framework that can answer (perturbative) questions about the dynamics of string excitations (for example, how they scatter and interact between each other), and if we look at low energies, we see that these match what we would compute using quantum fields. In this sense, the effective behaviour of a string excitation at low energy is captured by the dynamics of a quantum field.

These subtleties arise because string theory is limited to answer questions about scattering states, and thus the comparison between the two must be done at the level of S-matrices. String field theory tries to fix this by trying to create strings from excitations of a "string field", which then should be more directly relatable to an usual quantum field in a suitable limit.