I know one thing, Tiago was shite at Chelsea. But then again, good at Lyon. I'm confused.
Perhaps I can help to banish your confusion.
The answer to your problem is Chelsea FC. Even though they have won 2 league titles in the last 3 years and finished runners-up in the 3rd, you really have to be a student as to why certain players, Ballack, Shevchenko, Tiago, Wright-Phillips (and plenty of others) fail to shine at the club.
In a nutshell, the players previously had, at their previous club, a distinct role mapped out for them by the coaching staff as part of overall team strategy.
For example Shevchenko had superb rapport with his midfield, Pirlo, Gattuso, Kaka and so on. His movement was natural because the Milan tactics were second nature to him.
Compare that to the uncohesiveness at Chelsea where Shevchenko was given third rate service from the likes of Lampard and Mikel.
The same applies to Ballack who had a more clearly defined role in Munich. He has confessed to not understanding the Chelsea style of play and probably deeply regrets his move to the London club.
Tiago leaves Chelsea, miserable because the tactics are second rate, and, arriving at Lyon whose play is similar to the best on the continent. A style he can appreciate.
Remember, Chelsea won their titles
in spite of their dreary style, not because they were fluid in midfield and attack. They had a superb defence and relied too much on Robben and, of course, Drogba.