Is the Jail-Break roll for this mandatory? Since it occurs in the Arkham Encounters phase usually I would think yes but The Jail Cell doesn't really seem to be a true location in so far as you cannot move there. In addition all the encounters in the Jail Cell are geared for the escape action only. Also thematically it seems to be that an investigator should be able to choose when he wants to try since you may want to wait until another investigator moves to Sawbone alley first.
Also it would seem that you could try to escape the immediately following AE phase just after the movement phase you got arrested though you would still be delayed next turn. Does all this sound correct?
Check this thread out for a bit more discussion.
http://boardgamegeek.com/thread/1000560/innsmouth-jail-cell-question