I married a K1 immigrant, do I need to physically live with her?

There is no requirement that spouses must live all the time with each other. There are reasons why spouses sometimes are physically separated (such as because one is working overseas or serving in the military). However, living separately may cause problems in proving having a bona fide marital union. You two may not have as many opportunities to present each other as husband and wife to your friends and relatives or take pictures doing things together. You must find ways to prove that you two have a life together. You likely will need to document that you two travel to meet each other as frequently as your work schedules allow. Sometimes USCIS investigators come to your residence to check for signs that you two are living in the same place. Even though you are working overseas, in a bona fide relationship, there likely would still be many signs of you sharing the some household (such as pictures, sets of clothings, etc.) You should review your specific facts with your attorney for more information.

The problem here is that when you are not actually living with your spouse it does not really lend credibility to the bona fide nature of your marriage. You may be able to prove that your marriage is bona fide even though you are not living together. You will have to attend the interview for her adjustmet of status. You should consult an attorney to discuss what types of evidence you need to submit to support the legitimacy of your marriage and how to handle the interview.