What do you mean by the lifters are tight? Tight in the bores?
A couple of points....
Make sure that the "free movement" that you're taking up is indeed free movement...i.e. the pushrod not making contact with anything. A lot of guys will tell you to go by how the pushrod spins, but that's a false sense of security. I prefer to move the pushrod up and down axially while slowly tightening the adjuster, until you feel all the slack being taken out. You have to be really careful with your feel here, because if you're not careful, you can be depressing the plunger on an empty lifter.
A cold engine with a cast iron block and aluminum heads will not affect the running preload enough to matter. It will be about .006" after it's all said and done.
Lifters will do silly things, depending on whether or not the oil has drained out of them. If the oil has drained out, then the plunger will be loosey-goosey in the lifter and you will be able to move it freely. If the oil has not drained out, then it will be like....well....trying to compress/move oil when you run the valves. It's very common to see the valve drop. If you have ran the valves correctly, the valve will slowly close as the spring pressure pushes the oil down in the lifter.
If you can push the plunger down in the lifter immediately after running the engine (when the lifter is primed and the oil should be pushing back up at you), or the lifter is ticking, then you have a bad lifter.