Just want to confirm how these strategies play out.
The strategy matrix asks for two military and one league issue. The second military issue notes that it is to be placed in the owning city-state space and used to build forces - one presumes this would happen first, then there would be an expedition, then a base would be built in the enemy's area.
But, under the implementation notes, the first action is the expedition, then base building, then a raid.
Both sound good.
Which way should this be played?
First off the chart is correct, but the Raid depends on whether the target city state is Enemy controlled or contested. See the note in the issues column  and . Once it is contested the Raid occurs. If this is the first such invasion, it is less effective. However, if the other faction is an active player (you) then you can add in another military expedition.
Second, remember that by the time the third issue (second military) is placed in the friendly city state there are now at least a dozen issues on the map (assumes 'Bot rumor markers are included). From experience this should allow this issue to be implemented prior to the attack, but if not, you send in the army and then the city state raises forces to replace the forces that have already left.