Why my birthday in the calendar lunar chinese is in May if I born in June?

Martin, your birth date should be calculated on solar calendar. Solar calendar is based on the earth's journey around the sun. However, Chinese lunar is based on the moon's journey around the earth. You can see that different algorithm is used. That's why the difference occurs. But it's said that they will coincide every 19 years. So it's possible that your birth dates on solar and lunar calendar might be in the same month.

The real birth hour is calculated according to the clock.

Thank you for your prompt response.
Is that there are pages that ensure hours happens a change in the signs, ie: 00-01 Rat (Beijing) *
It is advanced or decreased depending on when your origin, I live in Spain and there is a difference of 5 hours.
Others say as I told you the real time is solar hour and it must therefore be adjusted for summer hours, I mean if I born at the 18:00 the save daylight in Spain is +02:00 hours, then the real houra is the 16:00.