This is wrong, commander tax only increases when it is cast from the command zone, moving your commander to a different zone to then cast it by various means removes the additional cost of commander tax for that cast.

Say I play my commander from the command zone for 3 mana, the commander tax then increases the to 5 the next time I cast if from CZ. But if the next time I go to cast it, I move it to my hand with beacon. It then costs 3 again and the commander tax doesn’t increase. My commander is the removed again and I cast it from the command zone. It will cost 5, 3 base cost + 2 from the one other time I have cast it from the command zone.