I'm not exactly sure I get your question, but I think I can explain some stuff.
I'll be assuming your table is a bit like this:
date_added | some_data | some_more_data
------------|-----------|----------------
date | data1 | data2
As I understand your goal is to fetch all the rows that were added to a table the day before the query is run using a select statement. but your current attempt fails at doing so by also returning today's results.
Here is what's happening (I think):
SYSDATE doesn't just give you the current date, it also gives you the time. You can see that for your self by simply altering your current session and setting the date/time format to one that includes both time and date
ALTER SESSION SET NLS_DATE_FORMAT = 'DD-MON-YYYY HH24:MI:SS';
The reason why you would be getting today's rows is simple, your query is asking for all the rows who's date_added field is between right now and right now - 24 hours. Not today and today - 24 hours.
So what is the solution?
Use the TRUNC function to trim the SYSDATE to the day instead!
https://docs.oracle.com/cd/B19306_01/server.102/b14200/functions201.htm
SELECT
T.*
FROM
MY_TABLE T
WHERE
T.DATE_ADDED BETWEEN (TRUNC(SYSDATE,'day') - 1) AND TRUNC(SYSDATE,'day');
As you did mention timezones being a thing keep in mind that SYSDATE returns the date on the server itself and not your computer's.
More on that here: https://stackoverflow.com/a/17925834/7655979