Putting two hands together is simply a matter of coordination. One of the most common mistakes a beginner might make is to keep trying to play through a piece from beginning to end, attempting two hands together, no matter how laborious it becomes. Practising like this can really tire you out and doesn't really help as much as you might think. If it takes half an hour to play through the piece like this, your brain will feel like it has been put through hard labour and will still struggle to remember everything you just worked through.
Instead, I would tackle the problem a different way. I would suggest learning each hand separately until they each become reasonably fluent. This will encourage muscle memory, visual memory, aural memory and last but not least, mental memory.
After this point, I would then attempt hands together just one bar at a time or possibly leading into the first beat of a second bar. Then repeat. And repeat again. Doing it this way gives your brain a chance to catch on to what you are actually trying to do. I have tried this with total success with my own students, especially adult students, many times. So often I hear a student say, 'I can't put my hands together'. And at this point, I ask them to repeat the same section three times before moving on. The results are instant and always successful. After repeating one bar three times, we can move onto the next bar and do the same again.
I don't think it is a typist's bug. It's just a matter of allowing your brain to fully grasp what it is you are trying to do. After several repetitions, memory begins to kick in and the results can be startling.