When Doggett is in the alley with Lukesh, two police cars are pulling into the alleyway. However, when Doggett and Lukesh make the jump to the parallel universe, there was no investigation/sting against Lukesh at all, therefore no police or FBI presence around the apartment building. Ergo, the police cars not being present is meant to be the first clue that they've jumped universes.
Follmer is put in charge of the investigation so this might explain him giving orders to Skinner.
A number of times throughout the episode Follmer gives orders to Skinner as if Follmer is his superior, which he is not. Follmer and Skinner are both Assistant Directors, they are of equal rank/position within the hierarchy of the FBI, so Follmer should not be giving orders to Skinner and Skinner should not be acting as if he is outranked by Follmer.