You wouldn't really be using TB if you are using a DP adapter.
Are you sure HDMI has the bandwidth to handle boths screens?
In theory it is just a normal HDMI signal. HDMI splitting if I get it right does not more than duplicate the output to multiple screens. Not what I would consider a dual monitor setup.
It is not splitting as in two seperate outputs.
You are more likely to be successful with DP but even there I think Apple is still using the old DP which doesn't support daisy chaining.
If one screen has only limited bandwidth requirements (no video, games) than a USB solution could handle that one monitor while you normally use the other one. Not exactly cheap but USB 3.0 can handle quite a bit of detail now.