That's indeed how it goes. And you're right, 10 soldiers can be trained per psi lab.
Psi strength tells you how resistant your soldiers are against mind controlling (or panicking because of psi attacks)
The other "psi" figure (I believe it's called psi skill) indicates how good they will be at mind controlling aliens. Once you reach 70 or more, they're getting good. Above 90 or so and you can MC about any alien with a single attempt.
Once you're making enough money (laser cannons
) recruit loads of soldiers, send them to psi training at the start of the next month. After a month, sack those with bad psi abilities (mainly low psi strength, you really want them to be resistant to alien psi attacks).