Hello and Welcome -
My name is ***** ***** Im happy to help - Sorry you have had a wait.
It is true that if what they are saying is correct, you would expect at least one fault code - if not two. But then maybe they did get that but didn't bother to elaborate to you.
If the hot and cold sensors are the "wrong way round"... Im assuming they mean the wires to them are back to front - ie, all thats needed is to swap them over... but it could be that the sensors have physcally been fitted back to front - in which case, all thats needed to remove and swap them both... It doesn't make sense that either job would come with a quote of 1300.... I assume you mean dollars!.
What I would do is go back to them - as you have the right - and ask them to show you physically whats what - what the problem is - and exactly which sensors they refer too.... Then question them on the price...
Too -once you know exactly then whats what - if that's all it is as above, you can do it yourself - or have a local shop swap them if you cannot... its not an expensive job - that just doesn't make sense.
-- As a further tip... the Mazda you have wouldn't really benefit from a "tune up".. there is really nothing to do.. not on the tuning sense of "yester year"... Older cars with petrol carbs...and basic ignition timing etc could be tuned but anything post 2000... such as yours , there are no adjustments that can physically be made. The fuel system is injection and cannot be adjusted - as too the ignition system / timing is electronically controlled too, by the ECU - engine management computer.
So really all you can do is have an engine service done - which replaces the spark plugs - ( and oils / filters ).. and thats all thats needed to keep the running tip top. I mention this just as a tip / to help you understand the systems.
- -But as for the issue you raised , follow through on the above as I have outlined to get this sorted out for you.
Let me know how you go..and / or let me know if you need anything further on this.. I will be only on a little today due to other commitments but will always get back to you asap thereafter if needed.
~>>~~>>~ Meanwhile now at this point- Please do click on the "Exc / Ok rating" for me at this time.. "Thank you" in advance for that .
.. Note that you can get back to me anytime at all after doing the rating - it doesn't close you out --
Best Rgds, MIKE