An executor not only has a right but an obligation to inventory the assets of an estate including the residence and the contents therein. On a personal level, there can be an argument that notice should be given prior to the executor entering the home in which you have resided. However, any legal basis is contingent upon your right to live there. If you are to be the owner of the home, the property is considered vested in you even if the deed has not been transferred to your name. To be safe, I would request that the executor provide reasonable notice prior to entering the home again. I would follow up this request with a confirming writing. Good luck.
This response does not constitute the establishment of an attorney-client relationship. It is also not to be taken as firm legal advice as such would be contingent on a full inquiry by the attorney into the complete background of the facts and circumstances surrounding this matter. The response is meant to be a helpful guide to a question in a manner which reflects the limited information provided by the inquirer.
This is a quasi estate question, but calls into question the rights of landlord-tenant. While the house becomes yours following probate, until the probate is over, it belongs to the estate. Because you are in possession, you have rights. You should contact a real estate attorney in NJ. While the executor has an obligation to take possession and control of the decedent's property, they cannot invade your privacy in this manner without notice (I may be wrong because of NJ law, but do not believe I am).
You should notify your sibling not to do it again, and that you are more than willing to cooperate and will make access available upon reasonable notice.
The general advice above does not constitute an attorney-client relationship: you haven't hired me or my firm or given me confidential information by posting on this public forum, and my answer on this public forum does not constitute attorney-client advice