I use a specific style for table anchor points, imaginatively called :anchor and defined as left justified. Sometimes I import tabbed text for a fairly narrow table, and convert it using a table style defined as left justified.
How come the results (in this special case of a narrow table) float airily to the centre of the page, ignoring the "left" setting for both the table and its anchor? What's the trick for forcing a narrow table to line up with the lefthand text margin, apart from widening columns until it decides to jump?
If you place the cursor within the centred table and open the Table Designer, does it actually have the Left setting?
A screenshot (wih Broders & Text Symbols enabled) would help.
This may or may not relate to your case...
Does your text flow allow for side heads? If so, then if your table anchor is in a paragraph that is in the text column (that is, NOT in the side head), then the table will also be in the text column IF it is narrower than the text column. Such a table aligned left aligns at the left side of the TEXT column, NOT the left side of the text FRAME. If you make the table wider than the text column, it will align to the left side of the text frame.
If you want a narrow table to align with the left side of the text frame, then put its anchoring paragraph in the side head.