How are you doing the installation?If you install via board manager or manual install by extracting the manual installation version of the board package into the hardware folder inside your sketchbook it should "just work"
I should have asked, in between switching which core you're using (TinyCore or MegaCore) are you changing anything in the 'Additional Board Manager URLs' field?
Yes sure. To install the other Boards I have to change the link in Additional Board Manager URLs field. And then... the other Boards are gone :-)So, I can only have one type of Boards, ATiny or Atmega16 :-)
Im using these URLs:ATmega16: https://github.com/mcudude/MightyCoreATiny: http://highlowtech.org/?p=1695