I have a Mac Mini, which came with a 2 Gb 1333 MHz PC3-10600 DDR3 SO-DIMMs but I already tried to upgrade with 2 kits:
And after I installed both upgrades, the Mac Mini does the chiming sound repetitively. But when I put the 2 Gb stick back it works. Am I missing any step or just being unlucky with the RAM sticks?
While this answer is a bit dated (25 months as of this answer), I wanted to close the loop so to speak and provide an authoritative answer for future readers.
The continual chiming sound is indicative of a memory issue; also proven by reinstalling the original SO-DIMMs.
Bad memory slot(s). It was never mentioned whether the configuration was two 1GB modules (default) or a single 2GB module. If one of the memory slots are faulty, then the system will generate the “bad memory chimes.”
Faulty memory modules. According to Everymac.com, the memory specifications referenced in the OP are correct; nothing was missed. However the no-name/obscure nature of the memory manufacturer (Timetec) raises red flags. This looks like it could be knock off memory sourced from China. It’s always better to purchase branded memory for best results.
For this application, I recommend Samsung PC3-10600 SO-DIMMs (16GB Kit).
Improper module installation. It goes without saying that a misalignment of the module in the slot, can cause memory errors. A simple fix is to reseat the modules. It’s also a good opportunity to clean the contacts in the slot(s) with isopropyl alcohol (91%) using a cotton swab; make sure everything is dry before reinstalling.
Presumably, this is a 2011 Mac Mini? That's the only one that takes that speed of memory.
Macs (of that era) make different chimes at startup if there is a problem with the RAM.
So,
Another possibility is that the RAM is slower than the computer requires. Sometimes, it will still work, but sometimes it won't.
