Strategic form: mixed strategy nash equilibria?
The probability vectors you gave in red describe pure strategy NE. (They assign probability one to an action.)

$\tau$ shows the probability that the column player plays action $l_2$.
If $\tau = 1$, then he will play $l_2$ with probability one. This is essentially another way of saying that he plays the pure strategy $l_2$.

One way to get these probability vectors is to find the PSNE as you have done. The PSNE $(u_2,l_2)$ means that the Row player plays $u_2$ with probability one, and the Column player plays $l_2$ with probability one.
According to your notation this means that $(\tau, \sigma) = (1,1)$.