One of the reasons that Uniocode was developed in the first place is to make this kind of workaround obsolete - to give each glyph in each language its own codepoint. You've installed the fonts correctly, I'm sure. So the software would think it was a lowercase j, and you'd whack J on your keyobard to key in a Tamil letter ta. We'd take a Latin-script font and empty it of its glyphs, then put in new glyphs for our target language. See what I mean? The encoding in Baamini is what we used to do, back in the Bad Old Days, to work with non-Latin-script languages. It's a pre-Unicode font. Take a look at what the Glyphs menu reports when I highlight the same character set in Baamini and in Latha.
I'm fairly certain that you've installed the fonts correctly the problem here is that Baamini isn't a Unicode font.