I work for temp agency located in Detroit suburbs where is no city tax. All my work assignment and all my pay I get straight from them. They send me for work to a city with city tax, now they started deduct the city tax from my paycheck. Is this correct?

BTW, I don't live in that city either.

I guess in general yes; you mean the city with city tax deducted the city tax form you r paycheck?? Then yes. The city ,since it pays you, needs to deduct city tax from your paycheck. You may contact the city taxation jurisdiction for sure.