Hi gargamel9
You should see the upgrades on your combat tab of the crafting window, right next to light armor. The recipes are very simple - they should be visible immediately on a new game, with no research required to see them.
I'm not particularly familiar with the Yuoki series of mods, but as long as vanilla light armor and heavy armor are still there, TinyStart armor should work just fine. If the aren't, then that could be the problem. If you can list your exact mod setup I can take a look at it.
Also, obvious though it may be, it still may be worth double checking you're on version 0.16.6 of TinyStart, and didn't end up getting an old version stuck in the mod folder somehow. There's also a few other uploads of TinyStart around, as I wasn't available to update it immediately for the game version 0.16 when it released; if you have one of those, of course, it will be out of date.