Hello there! I am using the version of Premiere that is current as of the time of this reply. I have figured out how to fix the position wherever you like. This is a general guide that I came up with to get nicely bottom centred text that anyone should be able to easily adjust. The bold is the important bit. The rest of the text may not be needed for more experienced users, but the UNBOLDED TEXT AHEAD may contain helpful tips
HOW TO:
There are nine small squares in a grid like pattern. Ensure the bottom centre box is filled in (if not, just click around it a few times until it is).
No need to touch the XY percentages. (The rightmost percentage should already be at the highest point, meaning if you try to hold click and drag it any higher, it won’t go past the number where it is. Alternatively, if you try to type a number that’s higher than the max, it should just immediately go down to the max, if that makes sense?).
Now, click on the captions (the purple bits, not the black bars within the purple bits) in the timeline and go to the “Effect Controls” Panel.
Set the rightmost number of the “Anchor Point” to 500 (or whatever you think is best looking) and voila! You can easily change the XY position of all of the captions by simply changing the Anchor Point numbers. If things look a bit weird or off centre after changing the anchor point, ensure the centre middle box is still checked.
Hope this helps. I came here earlier today and didn’t exactly find an answer, but found this out and wanted to share the things I learned!