That would be the client side yes. You need to send a packet to the server (all this packet does is say "this button was clicked"!) and the server does the operations neccessary (including checking to make sure that the player is allowed to click the button).
Quick "Am I on the Server?" guide:
Is it visual? No, you are on the client
Is it input related? No, you are on the client
Was a world or player object passed to you? Maybe, check world.isRemote (or player.world.isRemote)
isRemote returns true? No, you are on the client
Did you get your world by calling Minecraft.getInstance()? No, you are on the client. Also don't do this unless you know what you're doing.