You should not because on Earth, where gravity is relatively strong compared to the Moon, time runs slightly slower due to the gravitational time dilation effect. This means that clocks on Earth tick slightly slower compared to identical clocks in a region of weaker gravity, such as on the Moon's surface. So the UTC is from Earth perspective.
From rough calculations, the time experienced on the surface of the Moon is 0.99999999999848 times the experienced on Earth
From rough calculations, the time experienced on the surface of the Moon is 0.99999999999848 times the experienced on Earth