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.