Cox internet connection Issues

Hi I need to ask a question I have 2 Internet accounts In my home one is for my son and one is mine I pay the maximum for each of them I have been having trouble with my internet connection going out on both accounts Cox sent out a rep and they found a lot of problems with the cable so they replaced it but they ran one line and put a splitter on it and then ran it to my Router/Modem I asked them to run another line from the tap so that there isn’t a problem with the other line we each have a separate Router/Modem could this be the reason I’m having problems with my internet connection???