Why does this happen and can I fix it?

Here's a tutorial on anchor point:

https://helpx.adobe.com/ph_fil/premiere-pro/how-to/move-anchor-point.html

Also see “Adjust or animate clip anchor points” and “Adjust anchor points in the Program Monitor” here:
https://helpx.adobe.com/premiere-pro/using/motion-position-scale-rotate-clip.html

Things that may or may not be clear: There are 3 anchor points in the effect controls for text – Vector Motion, Text, and Video. But the Transform sections of Vector Motion and Video apply to the whole frame (and by default are centered). If the text box is not set to the center of the frame, then even with its anchor point centered in the text box, it will not zoom correctly if using zoom/scale in the Vector or Video/Motion sections.

Another thing that may not be clear is that text is in a text box, and it behaves differently. There are two types of text boxes.

Point text is created by clicking with the Text tool and typing. The bounding box expands as you type, but does not word wrap. So the box (and text) will run off the screen to the right if you type enough. The Text/Transform “position” is the bottom left of the TEXT, not the bounding box. The Anchor Point is the same bottom left. But its number is zero, zero - an adjustment from position, not a position within the frame. Anchor points for Vector and Video Motion are expressed as a frame position. If you drag the bounding box, the text adjusts.

Paragraph text is created by clicking and dragging the bounding box before typing text. The text wraps as you type, and generally, the box does not change. The text scrolls out of the box and out of view. (My tests today had some exceptions.) The Text/Transform “position” is the left/TOP position of the bounding box. The Anchor Point is the same and with the zero, zero adjustment. If you drag the bounding box, the text does not change.

Many users are now animating text that comes from using the Upgrade Caption to Graphics function. So it is relevant that Caption text is “paragraph” text, and inherits that characteristic when using Upgrade Caption to Graphic.

Stan