In the Ch. 235 scanlation, Rakan is not with Negi and Kotario in the bath. Before Nagi ran into Fate, Rakan was another area in the city. At least, he was near the area where Haruna's ship was dock. It is likely that Rakan is nearby in the men's bath. Just close enough to keep an eye on Negi and Kotario.
I think that Rakan is in contact with Takamichi. Rakan has to be in contact with Takamichi thru a third person. A person who Takamichi and Rakan trust. The information which the AA has acquire on Fate is very important not to ignore. If Rakan is in the Men's bath, he can still have a meeting with Takamichi and his contact without Negi and Kotario finding out.
Rakan being in contact with Takamichi thru a third party does make some sense.