mjhjmtu

By power supply unit should ideally output +12 and -12V, however the readings are closer to 12.2V and -11.8V.

Is this likely to cause a problem, even though I only need an output range of 10V to -10V?

If your op-amp can swing within 2.2V of the positive rail and within 1.8V of the negative rail under all possible load conditions, and if the inputs likewise are within the allowable common mode range then there is no problem.

There is no requirement for balanced voltages. You can use -0.1V and +20V if that works as indicated above (and, of course, if the op-amp can handle a 20.1V supply).

The PSRR specs include DC meaning , other than saturation near the rails, if bipolar outputs , there is neglible influence.

If you operate within specifications your choice of +ve and -ve supply rail magnitudes is not that relevant.

Usually systems are designed with same voltage but this is not a hard and fast rule. Often we see a few volts negative to handle ground references inputs and outputs and the positive supply common with other needs. Supplies of +12V and -5V would be common for reliable 0-5V operation.

Your choice of OP amp or other components will dictate the power rails.

If you need to operate at the mid point of the output swing and want to amplify ground referenced signals then you need to keep them equal magnitude.

Some new OP amps can operate very close to the rails on input and/or output. These developments are the result of the drive for ever lower operating voltages. You cannot afford to loose 1.2V of headroom if your circuit is working with a 3V supply that you want to run from a single cell that is partially depleted.

Most OP amps with single and dual rail operating specifications are inherently designed to handle uneven supplies. One of them is by design specified to be zero. Bypass, compensation and other circuitry has to be referenced to the correct point, often the negative rail so it works in both configurations.