It is not necessary to jack up the first joist to get the benefit of sistering. The first joist is stressed because of the load on it, hence takes a deflected shape (all stressed structural elements bend due to the stress). If you jack the first joist back to level before you sister, all sorts of complicated things happen.
First off, the first joist has probably taken a permanent deflection, since wood is an inelastic material which takes a permanent set after it has been exposed to load for a year or more. You can see this in any old house, the floors are out of level, because the joists have permanently deflected due to the load. Even if you remove the load, the joists will NOT spring back to their original shape. If you force them back to their original shape by jacking, you are effectively prestressing the joists in the opposite sense of their deflection, so you may end up in a situation where the top of the joist is no longer in compression, it could be in tension while the jack is in place.
Then when you nail on a sister, you are locking in the reverse stress in the original joist, and you can get a wide range of stress results when you release the jack and reload the joist pair. Very complex.
If you do NOT jack the joist back up but simply nail on the sister, the two joists will share the load. They will share the load approximately evenly as long as the two joists are fastened together sufficiently well that the horizontal shear which develops when the two joists are loaded gets shared. The mechanism for horizontal shear transfer is the nails, bolts, or glue that holds the two together.
If you forget to nail the two joists together, whichever one is higher will carry all the load, until it deflects far enough so the second joist begins to pick up load. This is a bad plan, since the first joist could conceivably crack before the second joist picks up load, then the second joist can crack since the first joist is no longer contributing much strength. This type of failure has happened in industrial and commercial projects where two structural elements were not properly connected, and got loaded before the fastening was complete. Bad news, best avoided.