In layout setup, the Show Records From drop down specifies the table occurrence on which a layout is based. If your layout is based on Table B and you perform a find where criteria, such as the year is specified in fields from the related table A, you find all records in Table B that have at least one related record in Table A that match your criteria. In your case, that means all Table B records that have at least one record in Table A with the specified year.
The script then returns you to browse mode where your existing relationship between tables A and B controls what Table A records appear on your Table B based layout--the find criteria you specify do not affect what related Table A records appear, only what Table B records are now in your found set and thus you see related Table A records (In a portal, I would guess) for all kinds of different years. (But there should always be at least one with the specified year.)
To see only Table A records of a specified year:
1) Do the search on a layout based on Table A instead of Table B.
2) Use a portal filter to filter by a specified year.
3) Add a match field to the relationship between Table's A and B that allows you to choose a year and then only see related records from A based on that year.