You're upgrading your vBulletin forum or installing a new one?
Before anything else, do a Full Account Backup from your cPanel. You can never go wrong with a good backup.
vBulletin forums have many threads, topics and docs on installation and upgrading. You should read thru a lot of that to get you going in the right direction.
To the question of using the cPanel File Manager, unpack the vBulletin zip file you downloaded from vBulletin locally and go into the upload directory. Highlight all files inside, right click and choose add to upload.zip (if on windows for example) if on MAC chose compress items.
In cPanel File Manager, navigate to outside of public_html and create a workroom (name this whatever you like) directory to test in. Upload that compressed file to that workroom directory. Now click that file one time and then at top of File Manager click Extract. All files should now be displayed meaning it unpacked right there, not into a new sub directory.
If that's what you see, you're ready to go. (we've just tested that your file will unpack properly here)
Click that compressed file you uploaded, and choose Move. Move it to the directory the vBulletin is in.
Now go back to outside the public_html where you see that workroom directory and delete it. No longer needed, it served its purpose.
Jump back over to your vBulletin directory where you moved the compressed file you uploaded. Click that file one time and then choose Extract again here.
In doing so you're unpacking that compressed file and overwriting all files with newer versions. Once you do this, don't access the forum, instead open the upgrade URL as described in the vBulletin vb4_readme.html that explains the upgrade process.
From there, type in your customer number and you're off to the races.
That's all pretty basic stuff and not too hard to do. What you might run into are problems with out of date custom plugins installed on that forum. If you have none, no worries.
Doing the above can be accomplished in about 5 minutes or so. From unpacking that vBulletin zip, to finishing the installer/upgrade.
GL!