I have the same tester. It beeps because the -12VDC is missing or wrong. But that's not a problem. -12VDC is no longer a requirement. As long as the +12VDC, +5VDC and +3.3VDC are present, and within the allowed ±5% tolerance (and they are in your case). Then your power supply is fine.
So something else is wrong. Make sure all your power connections are tight and secure. Check your motherboard and graphics card (if using one) manuals to ensure all power connectors are used.
Note that cases are designed to support 1000s of different motherboards. So, it is common for cases to have more motherboard mounting points than boards have mounting holes. And while the ATX Form Factor standard dictates where motherboard mounting holes “can” be on motherboards, it does not dictate where they “will” be. So, one board may have a mounting hole in a specific place while another may not.
A common mistake by the less experienced and distracted pros alike is to insert one or more extra
standoff in the case under the motherboard. Any extra standoff creates the potential for an electrical “short” in one or more circuits. The results range from "nothing" (everything works perfectly) to odd "intermittent” problems, to "nothing" (as in nothing works at all

). So, you might want to verify you only inserted a standoff where there is a corresponding motherboard mounting hole.
So, if you are sure you made all the proper connections, I recommend taking everything out of the case and assembling the computer on a large, unfinished bread/cutting board to see if it boots there. Then inspect the case and verify again, only the necessary standoffs have been installed in the correct places before reassembling back inside the case.