We came . . . . . . . . the room and jumped . . . . . . . . the swimming pool.

We use 'out of' as a preposition to talk about movement from within somewhere or something, usually with a verb that expresses movement (e.g. go, come). It shows where something is or was going.
You can use any of the following preposition after jumped: in, into or over. 'In' and 'into' mean the same thing; 'over', of course, means that he started his jump on one side of the pond and ended on the other side. 'into' is more suitable preposition with 'jumped' when we are talking about river, lake, pond etc.