OS X 10.4 only went up to 10.4.11 so I would be a little leary of something claiming to be 10.4.12 and 10.4.13

I would probably be better if you were to repair your software update component of 10.4 by doing an Archive and Install of the system.

This would place a new system onto your computer and you would then update it to 10.4.11

Make sure you have a good backup before you start, just in case something untoward happens during the install. Power failure maybe.

P