In our experience it is normal for semen to leak out of the vagina after regular intercourse and using Mosie is no different. The quantity of semen is much more fluid than the cervix will allow through. The closed cervical entrance is actually a tiny canal that only things as small as sperm can fit through. That combined with increased fluid in the vagina at the time of ovulation just creates a lot of fluid that has nowhere to go. That's why we recommend elevating the hips/bottom on a pillow - it just helps keeps more in for a longer period of time.
You could try to push the syringe down more slowly which might help with the back flow. Also, although the syringe holds up to 6ml, 4-5 ml is an adequate amount to insert and probably the most comfortable.