I did not have a job when I entered the US on the K1. I resigned from my job before moving country.
I got married and filed the I-485, then a couple months later I received a job offer to work as an offshore consultant for a U.K. firm. Therefore, when the I-485 was filed I said I was not working.
I was paid into a U.K. bank account, and did not pay U.K. taxes on my income since I was on a consultant contract, with my US home address as my place of work/residence on the contract. Filed all of this income with the IRS using an accountant and had no problems. Was classed as self-employed income. No problems with USCIS either since no US work was performed. Feel free to dm me if you have more questions