One thing which would helped me a lot was to read the full datasheet before testing nothing, and I say that for this:

So I got an tpl5110, now is time to test how well it behave keeping track of the time. My setup was similar to the previous one, a clock, in this case the timer ic, an arduino for interface with the pc and a precise internet clock, for compare to experimental results.

This time I started to count at 16:41:00h, which is a total of 12610 seconds. As you can see this time I added more information, like how many time a tick last (because the TLP5110 requires to select a discrete time duration, I choose 600ms), how many ticks were being skipped (I will explain this in a moment) and the total tick count. I got 20926 ticks, with a duration of 600ms each one is equal to 12556 seconds, so is an error of 54 seconds, the 0.43%, much better than before, but quartz clocks are rated at 10-100ppm, which is 0,01% so I would look for other a ultra low power rtc.

How you can see there are some ticks skipped, so for solving it, the TPL5110 have an input pin which when the uC get the tick right, turn it on for telling the timer that the signal was successfully received. It reduced the skipped ticks to a total of 6, so successful, but I got worse accuracy, a 0.7%

The accuracy was written into the datasheet, I should had read it, so in conclusion, I can handle a 0.43% of error (6 minutes a day) for my initial prototype, but I have to start thinking in to looking for a better timer ic.