Final Cut was transcoding (converting) your footage as part of the import process. Premiere is different and works directly with the original footage, so it is not going to get any larger. Works natively.
Please look at the Premiere interface and at the lower left area, look for a TAB that says "Media Browser" and click it - this is where you will import the AVCHD footage, NOT via File > Import menu.
Good luck
Jeff
