Grond and earth tingles

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If you have a multimeter do a continuity check between the ground screw terminal on the PSU and the earth pin on the mains plug feeding the PSU. You should get low resistance (less than 1Ω). If you do get continuity, check if the USB connector metal shields are also grounded properly using the same technique.

You should connect the power supply ground to the earth for the 24V, 12V and 5V.

The tingles come from at tiny leakage current and if that it grounded there will be no problem.

Either the unit isn't actually earthed (so you're getting leakage as if it's acting like a Class II device instead of a Class I), or it IS earthed, and it's you who's charged up, and discharging to earth via the casing.

MANY years ago, a crude and simple earth test for a socket was to have a 60W bulb wired to a plug, from Live to Earth, and when plugged in the bulb should light brightly. This has long since ceased to be possible, due to 'modern' earth leakage trips.