Wilson current mirror analysis
You got it partially right. The wilson mirror will reflect the reference by physical propriety of the transistor junction. The following relation show that:
\begin{gather}
\frac{I_{0}}{I_{ref}} = \frac{1}{1+\frac{2}{\beta ^{2}}}
\end{gather}

In your particular case, you assume both transistor are identical physically therefore and because the beta = 100 you can assume:
\begin{gather}
\frac{I_{0}}{I_{ref}} = 1 \\
I_{0} = I_{ref}
\end{gather}

To have that relation, you need that the beta of each transistor equal and both transistors to be matched.