This happens because the time you have calculated (70s) is the time taken by capacitor to reach from 1/3 Vcc to 2/3 Vcc. When you first power on the system, there is no voltage across the capacitor. That means it has to charge from 0V to 2/3 Vcc with the same time constant during the first cycle. And thats why it take more than 70s.
To avoid this, you should set the initial conditions on the capacitor i.e. before starting, the capacitor should have voltage just below 1/3 Vcc .