Thank you. I created a new build (not on itch.io, check http://voidroom.com/download/tea_v_0_3_13_198pre.zip ). There could be a few reasons that resulted in that problem and in this build they should be addressed properly. (manifest version, optional/mandatory setup, added a few more log statements to check if everything works fine). If you could grab it and let me know if it helps.
There still aren't any buttons bound. What did change is that "buttona" is no longer required to be bound.
I feel kinda stupid for not noticing until now but it seems when I save custom controller bindings that they don't get saved by Steam. I tried to create some custom bindings for Beat Saber and when I saves them it says that I am using custom binding in the controller menu. When I try to save custom bindings for tea.exe nothing appears in the controller menu just like when there is nothing bound at all. I also tested this for v.0.3.12 and the bindings are also not getting saved.
Log for #198pre https://pastebin.com/zPZZAF9F
There is now an updated http://voidroom.com/download/tea_v_0_3_13_198pre.zip . It should properly bind Index controller now.