Be aware that the inverter circuit will ensure that one of them is powered at all times - at start-up Q2 (mislabeled as Q1 in that diagram, the right-hand one should be Q2 - there are two Q1s!) will be on, and K2 will be on.
Using two pins you can have both solenoids off at the same time (or both on at the same time).
Up to you to decide which option works best for your project!
Should be fairly powerful solenoids to actually switch fast enough to make the 0.2 second interval. And indeed quite a noise. You're likely to need an external power supply to make this work well. Saves a lot of power spikes on the Arduino side, too.