The splitter is almost certainly the problem. When you've got sources going into a single input that you are summing together (if it is, indeed, summing) with a passive splitter, you are in for lots of problems. Does the splitter terminate in a stereo minijack or a mono minijack? Are the inputs on the cable for the mics mono or stereo? If it has any chance of working at all, the inputs for the mics need to each be mono, and the plug that goes into the camera needs to be stereo.
You don't necessarily need to go with something like a Zoom H4n (although an external recorder would be superior to the camera's audio recorder), but you may need to run a little line mixer or a preamplifier into the camera if you want it to work. The camera is likely getting confused trying to apply gain to the load of two microphones being passively split into a single input (if that's what's happening).
That said, a passive cable *might* work if it terminates into a stereo plug and isn't summing the two mono signals together. When two mono signals are summed the way you are doing it, you get all sorts of phase issues, the camera may see the load of the microphones incorrectly, there's just all kinds of things that can go wrong.
If you don't want to go for an audio recorder, you could get something like a Juicedlink adapter that will handle these signals correctly, and it will mount to your tripod mount.