I did a test and copied the .tfwx file, changed the name of the file to the second TIFF and that indeed did not have any effect on loading the second TIFF (still loads with the default coordinates). So, I did it using the alternative way, saving the tiepoints to a file, and loading that file for the second TIFF. Next did an Update Display followed by Update Georeferencing which did the trick. That would be an alternative.
However, I tried with another copy of the TIFF file. if you change the extension to of the worlfile to .tfw (yes loose the "x" in the extension) and load the TIFF, it actually loads correctly. For some reason the .tfwx file is not applied correctly.
Can you try again using the .tfw extension?