How does switching off pumps and putting on MAN switch resolve low pressure?
The procedure switches off the pumps, thereby resolving the low pressure. Low pressure means the pump is running but it is not pulling anything.

Fuel pumps can't draw fuel if the amount is too low. Imagine pumping water out of a swimming pool by attaching the pump to a hose. There will be smalls amounts that the hose can't reach. That amount is called unusable fuel and is part of the plane's operating empty weight (OEW).

See: What are different types of weights of an aircraft?

Some fuel quantity indicators are calibrated to not count this unusable amount of fuel.

If the captain really needs those 200 kg, they it's their decision to add a lot more in the center tank so it would be usable without any problems.



RE: What about the reason for putting the mode selector to MANual?

If the pumps are selected off with the mode selector still in auto, this will cause an auto feed fault warning as the normal operation of the auto mode (which is what causing the issue in the first place) requires the pump switches to be on the on position.

What does the auto mode do? See: Why are the center tank pumps deactivated when slats are extended on the A320?