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When heat is running all heat should by nature rise, so the heat from basement system will heat from floor up/ Unit in attic will blow heat down towards floor and by nature rise to heat second floor.
In cool mode, cool air will fall in both cases so the downstairs blows the air upwards and falls back to floor while second floor blows air down to cool upstairs.
Heat should not normally be on of course on one system and not the other.
The normal design for a two story home is lower floor blow air up towards ceiling and second floor blown down towards floor.
My suggestion would be to get rid of the oil furnace and install a new high efficiency heat pump.Ducts should be fine though