Are you sure that the 3.5mm jack you are plugging into is input/output? It is completely possible it is input only. Which would make the mic impossible to use. Also, in some case, an input/output jack won't work with some headphone/mic combos.
First try your earbuds in a different device to rule out them being the problem. If they work fine, then check to see if the jack is actually input/output or input only.
Also, why the splitter? I am assuming your earbuds (if the ones shown in your link) then you won't need a splitter. Unless, which also effects the jack question I asked, you have an input and then an output jack, separate, and are trying to combine them? If that is the case, the connector could be bad. I would try that on another device as well. Something that uses individual input and output jacks.
Lastly, the most simple fix would be to get a 3.5mm to USB adapter. Something like this...
https/www.amazon.com/LZYCO-External-connector-Headphone-Microphone/dp/B018YV3ALM/ref=sr_1_9?ie=UTF8&qid=1486193340&sr=8-9&keywords=3.5mm+to+usb+adapter and then you can avoid all the issue, as a USB port is less problematic in such a case.