Imprecise shifting on a Shimano 9 speed set
There is no compatibility problem.
If the direction you have to shift twice in is downshifting (pulling cable, going to bigger cogs), that can indicate not enough cable tension. If it's upshifting, it can indicate friction in the cable/housing.
It sounds a lot like one or both (could be both) of the above are true. Misalignment in the derailleur hanger can also add to the finickiness of the adjustment, i.e. making it harder to get the chain to shift right and then stay in place without the ghost shifting. Excess pulley and pivot slop in the RD can also contribute to sluggish shifting. So can a B-tension screw that's too far out.