How should I deal with lumber size differences when replacing floor joists?
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.