Hello,
You are correct - so-called convolutions in deep learning implement cross-correlation and are not equivalent to the convolution operation mathematicians are familiar with. However, using cross-correlations in a network, as is the norm, or flipping the kernels first to correctly emulate the mathematical convolution would yield identical results because in case of the latter, the model would simply learn a flipped version of the weights of the neural net trained using cross-correlation.
Please let me know if you require further clarifications.