From the Laws Of The Game:

The offside offence is neither a foul nor a misconduct, players are never booked or sent off for offside. Like fouls, however, any play (such as the scoring of a goal) that occurs after an offence has taken place but before the referee is able to stop the play is nullified.Players that continue such play may be booked based on the referee's assessment of how significant or intentional the play was. One of the main duties of the assistant referees is to assist the referee in adjudicating offside — their position on the sidelines giving a more useful view sideways across the pitch. Assistant referees communicate that an offside offence has occurred by raising a signal flag. However, as with all officiating decisions in the game, adjudicating offside is ultimately up to the referee, who can overrule the advice of their assistants if they see fit.

So it looks as if the assistant can call offside, but not give it. The mistake from Chelsea was them complaining that the assistant stopped play by raising the flag.