It is not the sperm coming out, it is his semen. The healthy sperm escape into your cervix and uterus in the 20 minutes after he ejaculated. Your vagina is however closed at the top, so his semen cannot go anywhere but out.
After sex, blood leaves your genitals and your vagina collapses onto itself (like a flat inner tube or firemans hose). This will squeeze it out slowly. The heat inside your vagina makes his semen turn into a thin liquid. As soon as you get up, it will flow out. This is called 'flow back'.
There is no solution for it, it is the natural process. Use a panty liner to keep yourself clean and dry the next day.
The one thing that may help a bit is to lie on your back with your hips elevated (on a pillow) for about 20 minutes after sex. After that, most sperm left over in his semen is practically dead and the good sperm made it into your uterus.
Best of luck TTC!