Either Shivaay Singh Oberoi is too dumb or is really as clever, which was the impression given to us in the earlier episodes.
I would go with the latter. From what I understood of yesterday's episode was, that Shivaay is clearly not buying Om being illegitimate, based on which he questions Jhanvi. And the answers he got in return, what he has perceived of that, we do not know.
So, I would say he does have a plan in his mind. Firstly, even if that Dai ma is lying, then also the Kapoors can cook up some fake proof, like in the case of his fake DNA report. So that the Kapoors do not release the fake proof to the media, like they did in Shivaay's case, he played his cards accordingly.
He showed the Kapoors that he is divorcing Anika, in quite a realistic manner. And seeing Anika's outburst, Tia believed it as well. And Tia was so busy gloating over Anika's plight , that the bimbo did not notice Shivaay NOT signing the papers...
What I don't get is why did he tell Anika, that they will work as a team, when clearly he just cannot and will not share his problems and secrets with her to live up to his GREAT WALL OF SHIVAAY SINGH OBEROI reputation. If you trust her, then trust her completely , or don't. I guess, his ego does not allow him to ask for help