Yes, exactly this.
Also the same player played in different positions (example: Cuenca as a LWF or LMF) will chance the overall mentality. The player is the same, so are the tactics, but he may like one position better than the other.
IIRC It gives 9 TS if player has 3 bars for all the team instructions AND is played in a position in which he has 'A' ranking (this ranking was indicated by the position being highlighted in a more solid color) and it would reduce a couple of points if played in an unknown ('C') position or 1 point if played in 'B' ranking position.
If above is correct then, this is how the TS number is broken down:
- Each player adds a point for each link he has with current team instructions. (Max by this route is 7).
- Each player adds 0-2 points depending on the position he is being played in. 0 for 'C' Ranking, 1 for 'B' Ranking and 2 points for 'A' Ranking.
Thus, a player having no links and played out of position will not add anything to the team spirit at all.
The only thing complicated about this system was understanding how much points will be added to the TS if the player has 2 bars in the particular Instruction, I'll guess it should add 0.5 for that instruction, but this isn't confirmed. As more matches were played with specific instructions, the player learned them gradually. Although they did learn quicker if they got ratings of 6.5 or above.
Since, you have the game can you check if all of the above is still true. If it is, then we can easily answer the 'how to increase TS?' and 'how does TS work?' questions.