"he jumped me" can't be used like that.
When you jump, you jump to a place. e.g. "He/She/I/It jumped." Infers that the jump happened in the same position. "He/She/I/It jumped backwards/forward/on/to/in/onto/into/etc" adds a direction to said jump. There always need a "direction" for a jump.
"He jumped •ON• me."
So the difference between tackle and jump is:
Jump is the act of lauching yourself to the air with the force of your legs; while tackle is throwing your body against someone else or an object, generally with the intent taking it down. Like a american football player or a rugby player taking down the player with the ball, thats a tackle.
When you tackle, you tackle someone or something, therefore you can't use it like jump.
"He tackled me", "They tackled the player with the ball", "I tackled a tree". It always need an object.