RC Circuit Simulation gives unexpected transient response
Before the switch was closed the \$4\:\textrm{k}\Omega\$ resistor current was \$1 \:\textrm{m}A\$. 

And the voltage across the capacitor is \$V_C = 12V \cdot \frac{4\textrm{k}\Omega + 6\textrm{k}\Omega}{2\textrm{k}\Omega + 4\textrm{k}\Omega + 6\textrm{k}\Omega} = 10V\$

Therefore after we closed the switch the initial \$4\:\textrm{k}\Omega\$ resistor current is \$ \frac{10V}{ 4\textrm{k}\Omega } = 2.5\textrm{m}A\$
And after the \$5\cdot\tau = 1.3s\$ the current will settle at \$2\textrm{m}A\$