Gabriel,
the exercise you describe is NOT Tan Tui but rather (excuse the bad pinyin) Ching Jing Tsui - translated as “To Lift 1000 Lbs.” It is a fairly common drill for northern styles such as Zha Quan. It can build extremely strong and balanced legs - but it is also very hard on the knees - so if you have a knee injury - don’t do it.
Tan Tui - there are actually two sets of characters for this. They both have the character TUI - leg but the Tan may be slightly different. One is Springing as in a spring or coil spring. The other refers to a well known spring well.
The Shr Lu Tan Tui (10 line)is probably the oldest intact version. It is mainly used in the Zha Quan systems (Islamic Long Fist) associated with the Hui ethnic group. The Hui were well known for their fighting and many of the Hui systems such as Pao Quan, Zha Quan, Hua Quan, etc… use Shr Lu Tan Tui as a basic foundation.
Then you have the Shr Er Lu Tan Tui or Shr Er Lu Tam Tui (12 line). This one supposedly has different origins but there are indications that it came from the Shr Lu Tan Tui.
There are also recordings of Shr Ba Lu Tan Tui (18 line) and others.
The methods are similar. Each set (10, 12, 18, etc…) can be done emphasizing the single line or as they call it Chong Tan Tui.
Single line is where you do each line (1, 2, 3, etc… ) over and over …a line of Tan Tui 1 across the training area, around the room, etc…
Chong Tan Tui is more for demonstration purposes and preparation to go to longer and more complex routines. This method is where you do Tan Tui 1 - 1 repetition, then immediately do Tan Tui 2 - 1 rep, Tan Tui 3- etc… So, you do all 10 connected together but only one of each. The name implies a stake running through it - kind of like a shish kabob.
Which one you do is not nearly as important as doing them with good stances, understanding that each kick can be low, medium, or high, that most of the punches can be straight, hook, uppercut, swinging, etc…