Sounds like the adaptor is not what it needs to be (although the description suggests it is not what you’d assume was shown !) - I can assure you that the official Elektron splitter will only present sound in one ear, the left
So if you plug a headphone in the Tip feed you get the left signal to the left ear and if you plug the 'phones into the ring you get the right signal to the left ear - i.e. the right-ring is dropped as per a TS outlet - so if you are hearing in both the cable has used TRS sockets and these are wired to work better for a listener - the adaptor isn’t ideal for your use case
adapting this short moulded adaptor would be tricky, simpler to make your own, pick up the handy Elektron one or start again hunting for a suitable one