Hi, Aido4ever,
From your description of the issue few things are apparent:
- you have insufficient knowledge about power supplies and mains earth issues - this is very important SAFETY ISSUE and practical consideration
- you bought a power supply with isolated outputs and it performs as it should.
As for 1), please check this forum topics, Dave's videos about power supplies and mains earth issues with power supplies and oscilloscopes, isolated(floating) vs earthed power supplies, etc.
Again, this is very important issue and your questions shows that you do not understand it. You have to know your equipment so that you would be certain about both your safety and potential damage to other equipment by power supply.
How are you measuring AC voltage between GND (green terminal) on PS and +/-? Typical DMM has ~10MOhm input impedance and it shows
ghost voltage - it is normal behaviour with mains powered systems.
If you load this ghost voltage (some DMMs has low input impedance mode, like Keysight/Agilent U1272, some Fluke DMMs), it will go away. If ghost voltage turns out to be low impedance AC source (which is unlikely), you have a problem.
GND (green) is connected(should be connected) to instument chassis, which is connected (must be connected) to mains earth. Both green terminal are shorted together. It is normal and it should be so. Your PS still has independant floating channels - these can be made dependant by connecting GND (green) to either + or - terminals.
But before your do anything with PS, please educate yourself about these topics