InDesign's Paragraph Styles are a text attribute, not a frame attribute, so the applied Paragraph Style dominates. Even if you specify different Object Styles for different frames, and set different Paragraph Styles for each, it's the last Paragraph Style of the first threaded frame that takes precedence.
Think this through, and you'll see the logic. You can't change the style of a paragraph half-way through the paragraph. If a paragraph were to span two text frames with different Object Styles applied, that's exactly what your scenario would require.
As an exercise, create two text frames on the same page and fill each with placeholder text, using a different paragraph style for each frame. Give each frame its own Object Style, specifying one paragraph style to the first frame, another to the second. Now thread them. That should make it clear what's occurring.
In essence, an Object Style can force a Paragraph Style only if the frame is not threaded, and only if a Paragraph Style has not been explicitly applied.