It's most likely just friction at the nut when you bend a string, or even just from the strings moving a bit when picking.
The locking nut on these guitars is NOT made to NOT be locked. It has a fairly large area where the string comes in contact, by design, to allow for a good grip on the strings when the blocks are locked.
Just lock the nut and use the fine tuners just like you would if you were using the trem un-blocked.
This should solve your problem.
If you just can't deal with locking the nut, or if you're using alternate tunings often and locking the nut is impractical, you may have to invest in installing a regular, non-locking nut on your guitar. This will look strange, since there is a large rout at the nut for the lock, and it may not even stay in place because there is no wood 'behind' the nut, but barring that, I see no other real options.
I doubt it's the tuners, as long as you're tuning UP when you do tune. The tuners on Ibanez guitars (even a lot of the 'cheap' ones) are all either good, very good or top quality and should give no problems.
I'm going to stick with friction at the nut/string tree. Simple as that. :-)