So Q₁ is the total charge on C₁. Q₂ is the total charge on C₂.
This charge will be due to any initial charge ( Q₁(0) = V₀₁·C₁, Q₂(0) = V₀₂·C₂ ), and the charge flowing through the capacitors because of the switch, which we can call Q. So Q₁ = Q + V₀₁·C₁, Q₂ = Q + V₀₂·C₂.
There is no reason why Q₁ and Q₂ should be the same - for example, if V₀₁ = V₀ and V₀₂ = 0, then no current will flow when the switch is closed, Q = 0, Q₁ = C₁·V₀, and Q₂ = C₂·0 = 0.
This one is set up with V₀₁ = 2V, V₀₂ = 0V and V₀ = 4V which ends up with V₁ = 3V and V₂ = 1V, so Q₁ = 3 Q₂: