Can diseases be transferred through getting spit in your eye?

Usually not. Saliva generally has a low concentration of truly dangerous pathogens. On the intact corneal and conjunctival surface you have antibodies which neutralize many pathogens. Getting blood splashed into the eye is a different story which can transmit HIV and hepatitis. Just wash your eye out and you should be ok.
Spit to eye. After getting spit in the eye, it is possible to contract a bacterial infection. In theory, hepatitis and HIV viruses are found in spit but the risk of transmission would be very low in this scenario.