Usually the trainers last for about 2-3 weeks, though the languages with new alphabets (such as Japanese) will take a little longer than that. By 4-6 weeks, you should have pretty much all of the language rules pretty much internalized.
If you're going at the default study speed (which is 28 new cards per day), it would make the most sense to wait a week or two to begin studying vocabulary, though you are welcome to whenever you are comfortable with the pronunciation. The most important thing is to be somewhat comfortable with most of the languages' sounds.
There will be a point near the end the cards where you stop seeing new pronunciation cards (e.g. "K" is for "Koala") and instead begin seeing simple spelling and vocabulary cards. This means you have covered all of the rules for the language, and can definitely begin learning words.
Note: As of September 12th 2019, we no longer provide official support for our Anki based pronunciation trainers and word lists. You are more than welcome to still purchase and use them, but the support we are able to offer for these products is limited. For supported languages, these materials are already built into the Fluent Forever app.