The documentation appears to have been written by a non-English-speaking person. I won't waste my time trying to translate illiterate gibberish, but I'll try to provide a quasi-answer here that might be of some help to someone not familiar with the RPi:
The RPi lacks much of the power circuitry found on conventional laptop & desktop computers. This is due to the fact that RPi was designed primarily to be a low cost learning tool. You'll find no power on/off button on the RPi, and it has no sleep or suspend state.
Instead, to properly & safely remove power from an RPi, you must first issue a halt/shutdown/poweroff command. Following this command, the RPi ceases to be operational, and power may be removed without risk of file system corruption. However, the RPi will continue to consume power after the halt/shutdown/poweroff command. The only way for the RPi to reach a zero power consumption state is to disconnect the RPi from its 5V power source.
After the RPi receives a halt/shutdown/poweroff command, the only way to restore it to an operating state (reboot) is to power cycle the 5V input power. There are typically a couple of ways to do this, depending upon the model, but the method that works for all models is to remove the 5V input power, and then reconnect it.
With that in mind, let's now revisit the mystery statement:
This is not a UPS! The Raspberry Pi will restart when you connect it to the Pi.
We know the following:
RPi will restart/reboot from a halted state - or a powered off state - when power is applied.
Perhaps what your vendor/manufacturer is trying to say is that this HAT is not a UPS in the sense that it cannot power the RPi while the battery is being charged? But that's only a guess... it cannot be a definitive answer to your question because it requires an assumption - an interpretation - of what they wrote. However, it is self-evident that what they wrote is poorly-worded and confusing.
