Cutoff frequency of a first order recursive filter
That formula for the cut-off frequency is a very inaccurate approximation. In this answer I derived the exact relation between the coefficient of a first order recursive averaging filter and its 3-dB cut-off frequency. Note that in the quoted answer I used the constant $\alpha=1-b$. From formula $(3)$ in that answer we get for the coefficient $b$

$$b = 2-\cos(\omega_c)-\sqrt{(2-\cos(\omega_c))^2-1)}\tag{1}$$

With $\omega_c=2\pi f_c$ we get for $f_c=0.25$ a value $b=0.26795$.

The frequency response of the filter is given by

$$H(e^{j\omega})=\frac{1-b}{1-be^{-j\omega}}\tag{2}$$

The figure below shows the magnitude response $|H(e^{j\omega})|$, and it shows that the desired cut-off frequency is achieved with the chosen value of $b$:



Note that the 'EDIT' part of the answer quoted above also explains where the inaccurate formula for the cut-off frequency comes from. The following figure shows the resulting cut-off frequency of the filter as a function of the desired cut-off frequency when the exact formula $(1)$ is used and when the approximation is used:



Clearly, the approximation is quite bad and it only kind of works for very small cut-off frequencies. I see no reason why it should be used at all.