I don't think that it is fundamentally wrong for your ex to make the choice to let the kids be home unsupervised after school, and I don't think you are wrong for being concerned about it. This could be a great opportunity for you to work together to educate the girls about responsibility, safety, and what they should do in case of emergency - also to sit with them and have a frank discussion of whether they feel worried or lonely when they are at home by themselves after school. If they do, your ex may be more open to your suggestion of afterschool care. If not, you may feel more comfortable with things as is.
With this approach, hopefully your ex should stop deceiving you about babysitting arrangements to avoid dealing with your objections.