As Always, nothing is safe from a skilled thief who really really wants it.  not in the real world, not in this fantasy world.  The best we can hope for is to make it really hard to steal (which means someone has to be really motivated) and recovery after it's been stolen.  I'm also assuming heist movie level theft here, because that usually makes for more interesting reading :)

OK, now that we have that little caveat out of the way, there are tons of ways to rig security around things that do not rely on sight.  Humans have a bias toward that sense because that is how we evolved, but we have other senses.  

Smell:  Most animals, as far as I know, produce pheromones.  These can be detected.  For a high tech alarm system use a clean room type system to make sure the chamber for whatever valuable [Dingus][1] you happen to be trying to protect is free of any lingering pheromones.  Once closed, the chamber is sealed off and sensors enabled to detect anything scent related, triggering an alarm.  Bonus points if you can use the same system to evacuate the chamber with the would be thief inside, suffocating them.

Hearing:  I'm putting all sorts of vibration testing in this category along with various uses of ultra sensitive microphones.  Here is a more specific idea. Echolocation type pings akin to sonar.  Anything changes in the soundscape of a room, like maybe a person moving about, triggers an alarm.  Your evil mastermind bonus to this one is again, the room seals, and our would be thief is bombarded with super high decibel noise that would deafen them, or just the "Brown Note" (yes I know the [brown note was busted on mythbusters][2], but I'm having fun here so hush)

Touch:  this is where the whole range of pressure sensors go.  Everything from the Indiana Jones Idol pedastal to The floor that Tom Cruise sweat on in Mission Impossible.  Pressure sensors are pretty common, so this should be easy to do in a ton of creative ways.

Taste:  This one kind of goes with Smell, since it is all about chemical detection.  I really don't know what do do with this, unless you make the person trying to access your treasure chamber, I dunno, eat scotch bonnet peppers and then the High tech tongue analyzes the sweat as an identity key.  Pretty farfetched though.

The long and the short is that there are a lot of modern day tech things we can do that do not rely on Visible light to aid in our security efforts.
In fact, we could even use the idea of checking in with our other senses to set the story and just about any tech level or time frame, from bronze age to modern day.

Smell:  Dogs.  They bark when something doesn't smell right.

Hearing:  Dogs again.  Their sense of hearing is a lot sharper than ours.

Taste:  Dogs yet again, Hungry, angry dogs will eat intruders.

Touch:  No dogs here, but things like bead curtains in doorways make it hard to pass through silently.  Put spiky bits along the tops of high walls, Generally make it hurt to get to whatever you are protecting.

Finally, since I just watched Ghost in the Shell, How about shallow water?  Even someone who is invisible will make ripples in the water as they move or even just stand there.  Those ripples will be visible.  Disturbed water will make noise.

So your invisible people have just a small edge over normal thieves.  Testimony based on what someone saw will become circumstantial, so securing convictions will require an advance on other forensic tools.  They will be harder to trace in the immediate time after a crime, unless you have a dog who can give chase based on scent.  So yes, advantage, but not as much as you think


  [1]: https://en.wikipedia.org/wiki/The_Maltese_Falcon_(1941_film)
  [2]: http://www.discovery.com/tv-shows/mythbusters/mythbusters-database/brown-note/