It is underpowered because the 1060 needs a minimum of a 400W PSU. You then have to take into account the efficiency of the PSU into account, again, and it can offer on a consistent basis 280W. Take a look at the sticker on the side of the PSU. You could also take a pic. Do you see +12V? What's the number(s) directly below that. It should say something like 35A but it's probably closer to 20. That +12V rail i what feeds the GFX card.
What? A SYSTEM with a 1060 would need ~400W, not the 1060 itself. And a Corsair 450W can put out a lot more than 280. Even on a "consistent" basis.
He's not going to be using 300W. 95W and 120W is 215. The rest of the system isn't another 85W. He's going to be a lot closer to 250W. The OP didn't say if he's using the CS or CX 450W Corsair. 250W at 80% efficiency is 312.5, which is the most it would pull. I think the lowest efficiency is supposed to be 82%, which is just over 300W while gaming. That should fit inside your 350W UPS. But you are so close that if you've OC'd some, if you have a higher clocked 1060 which uses more than 120W, or if your PSU isn't as efficient as it should or your UPS isn't as good as it should be there is your problem. The UPS might be complaining of the power spikes modern cards have. A bigger one should fix it.
If you want to know what your components would draw from the wall....look at the specs of each component....add up the power draws and divide by the efficiency.
If the efficiency is 80%......divide by .8. 90%....divide by .9 and so on.
Nope, doesn't work like that. That will simply give you 80 or 90% of the number you figured. Remember that when dealing with efficiency like this the number will always be bigger, not smaller. Look above for the example of that. 250W, 80% efficient, 312.5W from the wall. Doing what you said to do would give you a number of 200W, which is wrong. I do it the long way because that's the way I learned first. Figure out the power draw, multiply that by 100. Now divide that by whatever the efficiency is. 80, 82, 85, etc. Remember that you need the expected efficiency at whatever load the PSU will have. The max efficiency of a PSU might be 88%, but that's at 40-75% load. If you bought a 750W PSU for your 250W load PC, you aren't at 40%. You need to use the lower 82% efficient number for the lower load.