The sentence, "Your father sounds very stingy" would be used to describe a man who is OFTEN or USUALLY tight-fisted with his money and not generous about giving. You would be expressing the opinion that he will continue to be this way.
If you say, "That (experience) sounds as if your father IS very stingy", you are saying you think the father is still tightfisted and ungenerous. Using this sentence, makes you sound as if you think he will continue to be stingy.
If you say, "That (experience) sounds as if your father WAS stingy" you are describing one incident in the past when the father was not generous, but perhaps you think he has changed.
Hope this helps