The accomodation where you are staying, will (or should), report your address to immigration. TM30 i think. As an example, i live in Pattaya, but went to Kamphaeng Phet for 3 months, and the room owner notified immigration i was staying there, as its their duty to do so.
The employers take you to the immigration department anyway, so hopefully it can be sorted all in one go. Hopefully because of the amnesty, it may be easier due to not having to leave the country