Invisibility is a power that all merpeople are shown to have. However, it appears that only natural-born mermaids have this power since Evie has not been seen using it. Zac has the ability because he is a natural-born merman. There is also a possibility that Evie has simply not "unlocked" this power yet. Zac had to wait for one more full moon cycle before he was able to use it so the same thing could happen to all human-turned merpeople except at a much later time. With this power, it allows the user to stay invisible, but it is only temporary.
The user puts their hand in a fist motion and turns invisible. It seems like the merperson is enveloped in a water bubble, which makes the user invisible. Merpeople are capable of staying invisible with legs or tails, in or out of water. Rita Santos is the only mermaid that seems to be able to use her powers to see invisible merpeople by using a hand motion, as it was shown when she sees Zac Blakely in her office after he stole the test.