Multisession reading and writing is a method used for a disc. It adds sessions to already existing sessions.
It's a method not so frequently used or advised, because it entirely depends on the system if you can read all the sessions or just the latest ones.
Every added session also adds another table of content, which can cause trouble or reduce free space on your disc faster than you might think.
Give the price of current discs, (1 euro per disc or lower) "it's not just worth fussing about". Just make single session discs containing 700 MB or 4.5GB of data. At least those can always be read in about every device these days.
It does not say anything about the kind of discs you use.
Writable compact (CD) or digital versatile discs (DVD) can be generally specified in two kinds: Single Writable (Also known as WORM or Write Once Read Many Times)
ReWriteable (Also known as RW. Can be erased at least 100 times).
In your case you might think the disc has renamed or overwritten files, but you are probably only reading the latest session.
A good way to test this is to make another session with a single file that has a name that's not used in the previous sessions. If you, after writing, only this one file, you know it's reading only the latest session.
If your software reading all the sessions of a disc at the same time, you should be able to see any file, including the new one file you just wrote. It sounds logical that the os should pick the latest version of any duplicate file. You can also test this by writing a 1-byte file with the same name as a file on a previous session.