This site teaches the letters "eaint" first. I think it's better to introduce the home row first. Don't worry that you can't type much English with the home row (unless you're using another layout like dvorak). Just get them good with different combinations of "asdfjkl;". Then once you have that, you introduce new keys by having them practice the jump from the correct home row key typed with the same finger to the new key and back. Let's say we're introducing 'e' next. The exercise would be something like this:
ded ede dde eed eded dede deeded edded ...
This gets them familiar with precisely the right motor recruitment pattern. The point of this exercise isn't to achieve the absolute maximum speed. It is to exercise the movement pattern of moving a certain finger from the home row to the key and back. Obviously you need to make sure they're keeping their hands on the home row and not typing d and e with two different fingers to go faster on this particular exercise. But that shouldn't be hard to do in your instructions. You can start to dissuade this in your next exercises by bringing in the home row letters typed with the adjacent fingers.
fesd sefd sdfesd fdsefd ...
I think this kind of exercise pattern should be used to introduce all the keys. Once the student has established these motor patterns in the process of learning where each key is, then you can go on to English text. Of course you can put English into these exercises when possible, but not to the detriment of the main point which is motor movement patterns.
If you already know how to touch-type and are learning a new keyboard layout, then obviously you already know the motor recruitment patterns and the approach used by this web app is great.