In iTunes > Preferences > Devices

Down the bottom, is there anything that suggests that iTunes is pair with any remotes?

If so, forget them.

Try uninstalling Candleair, and disabling the remote in Plex.

Then quit and restart Plex (maybe the mac).

Test to make sure nothing is happening

Enable the remote again in Plex.

Test

Then maybe try installing Candleair again.

I remember Plex had issues when I used to use it where I had to forget and add the remote to get it to work.

Out of interest, if you do not have Plex open and up press keys on the remote, does that also start iTunes?

Sorry to be so vague, but that's the art of problem solving :)

And there are other media apps that start and stop itunes (mplayerx) that you might want to check, but if they are not running then they shouldn't interfere.

Good luck