I would suggest keeping them inside a greenhouse, or enclosure with artificial lighting to hold in the humidity. When they are first sprouting, they need humidity and moisture, and are vulnerable to drying out. But pretty soon they can become vulnerable to root rot if there's too much moisture in the soil. It's a narrow range, so it can be difficult. I would suggest using larger containers, that are bigger than how far the roots expand out. More soil volume helps to keep the soil moisture level more constant, so it doesn't dry out or get too wet. For example, a 3-inch high seedling might need a 8-inch wide container. 8-inch high seedling, then 12 foot wide container. Make sure to use good quality soil that's both good at holding moisture but won't hold too much water. Also for young seedlings, don't expose them to full sun. Their small root systems can't handle the water draw from that level of evaporation. Make sure the soil is fairly loose too, so there's air in there for the roots. You know there's too much water if the water has displaced all the air in the soil. Roots need to breathe, as well as moisture.
Pulasan is also the most tropical member of the lychee family, so I would keep the temperatures from going down too low. (maybe above 67 all the time, and usually in the range between 77 to 86 degrees Fahrenheit)