Don't mess with the PSR E-433. Use the keyboard default settings. Then set the MIDI track input to the keyboard Omni or channel 1.
The TTS-1 can play up to 16 channels. Starting with output channel 1 makes sense but it is not necessary. By convention channel 10 is for drums but the TTS-1 does not care about the convention.
I am sure there is an historic reason for the bank name but cannot tell you what it is. BTW, if you prefer, it is possible to set the instrument directly in the TTS-1 by clicking the EDIT buttons at the top of the UI and the click on the instrument name. All of the instruments will show in a popup menu.