Lets see, Ember Tetras seem to be tiny little fellows, fare better in a shoal of 6 and higher, only grow up to 0.8". The only thing I'm scared about is that if your Betta can fit one in his mouth he might, but they're probably way faster than him so no worries.
Lemon Tetras, same deal 6+, they grow a tad bigger though 1.6", really compatible like Embers, I see no problem.
Diamond Tetras, now these guys get quite big 2.4", plus they might fin nip your Betta's fins. But if kept in a small shoal 6-8 they'll keep the fin nipping inside their little group, but be careful.
Now I calculated with AQadvisor, if you have six of each fish, which is the minimum of a shoal you'll get a 66% stocking level, add in a Betta it goes up to 70%, so I'll say that you're doing just fine if you add in your Betta. Just watch to see if those Diamonds will nip him.
Either way, if it's heavily planted has a good filter, I really see no problems with adding your Betta in other than him getting stressed because there's too many shoals of fish, or that the diamonds are nipping him.
:] Good luck and keep us updated.