I believe the typical guidance is for the lines on a modem to be a home run to the tap. If it's split, it could throw the signal levels out of the acceptable range. In Five Aces pic above, the numbers by the outputs on the three way splitter indicate how many dB is lost coming out of that line. I'm not a cable tech, so I don't know what the range is, but I do know that if you're outside of it, internet won't lock, you could have picture loss on the TV (in an analog world, it would come across as snow or interference, digital signal loss means the picture is cut out entirely), or you'd have no dial tone for CDV service.
It happens, but your tech should be able to fix you up. Let me know how you made out in the end.