I am in the process of replacing 4 floor joists and the new 2x10s are 1/4" taller than what was previously there. I understand that as the lumber dries out it will shrink but how do i handle the 1/4" difference to have a level subfloor and not crack the tile i put on top.
I doubt your lumber will shrink 1/4" in width; it might shrink that much in length, but that won't affect your floor. Lumber has been cut differently over time. Just cut out a notch where the joist sits on the sill plate and center beam. If your lumber was too small, you would shim it, notching is just the opposite.
Once your subfloor is screwed or nailed with ring-shank nails(and glued to prevent squeaking) to the joist, there is little chance that there will be shrinking in a direction that causes any problems. Make sure you use quality flexible mastic under the tile and you will be fine.
I renovated an old house that had a variety of different thickness and width boards. You just notch and shim as much as you need to.
In my experiences there in no way to control how much a given piece of wood shrinks, that is if it has enough moisture content (MC) to shrink. If you could get it tested with a moisture meter for MC and it is around 6-8% preferably less, you can cut the joist to size for it will not shrink anymore. If the MC is 10% or more it will shrink and it will take a few weeks to get it to loose enough MC to not crack your tile. If you have kind of time to install the joists and wait for them to shrink in place in a heated environment, all the better. If you don't have that kind of time, then you will be better off purchasing LVL or other engineered lumber that does not move that much at all, unless it is really saturated.