The servo can only do what the transmitter tells it to do. If the servo arm is central with the transmitter sending "neutral" and without any settings telling it to behave differently, there should be an equal swing both ways. If the equal servo arm swing does not result in an equal tiller movement, then something is not properly parallel, or something is catching. I don't have one, but I've looked at a few, and things are a bit close in there.
Is it the Joysway lunch box transmitter with electronic trims or a more traditional one with mechanical slider trims? One I saw last year had problem handling that turned out to be one of the tiny slider switches that (if memory is right) had been set to "mix".