Is there any inrush current on the transformers?

Yes, when you switch on any transformer( or any inductor or capacitor)  there will be an inrush current but for a very short time if compared with motor, for example. As, in fact, the transformer on the time of switching will act as a short circuit path( low impedence path, Z = the ohmic resistance of the coil wire, which is most likely very low). But, as the magnetic flux develops in the core the reverse emf will develop, too, untill it balances with the driving line voltage. The inrush current amplitude depends so much on the at what time in the cycle the transformer is closed on the line. If the switching occured just at the wave zero crossing the inrush current will be negligible.