Relation between attenuation and loss tangent in EM wave propagation
The attenuation is given by
\$\alpha = \frac{\omega}{c}\sqrt[]{\frac{\epsilon'}{2}(\sqrt[]{1 + \tan^2\delta} - 1)}\$

The equation \$ tan \delta = \frac{\sigma}{\omega \epsilon}\$ assumes that the imaginary part of dielectric constant is 0, i.e. its a lossless non-ideal dielectric material, with non-zero conductivity. The more general equation for loss tangent is
\$ tan \delta = \frac{\omega \epsilon" + \sigma}{\omega \epsilon'}\$

Now, if you fit the frequency into the attenuation equation, you get square-root of the frequency in the denominator, while first power of frequency in the numerator. As a consequence, with increasing frequency, the attenuation is increases. Hence no contradiction.