The trainers generally last for 2-3 weeks (on the higher end for languages with new alphabets like Japanese) worth of new material. You should have all of that pretty well internalized by 4-6 weeks.
You can start learning words whenever you feel comfortable doing so. If you're going at the default speed (28 new cards/day), I'd say it might make sense to wait at least a week, maybe two, so that you can get somewhat comfortable with most of the languages' sounds.
There will be a point towards the end where you stop seeing new spelling cards (K is for Koala) and start seeing simple vocabulary cards ([Plays recording of "CHEESE" and shows you a picture] How do you spell this word?). You can definitely start learning words by that point; you've already covered all the rules, so new vocab is just going to reinforce them.