Tyre Pressure Monitoring Systems (TPMS) are useful, but can be a pain.
The i30 appears to use a so-called indirect TPMS (iTPMS). As indicated above, it compares the rolling speed of the four tyres front/back; left/right and diagonally. So each tyre is compared with the other three.
It’s simple, cheap, does not require any specific sensors… and inaccurate.
Imagine if you are going round a circular track. The inner wheels would travel less far than the outer ones, so the outer ones rotate more often, and so the iTPMS would indicate that the outer tyres are deflated.
Second, imagine a vandal has released the pressure in one of your tires overnight. One would hope that a driver would notice, but the iTPMS takes 10-15 minutes to detect that loss, due to the nature of the system.
A third issue is that in some countries, such as Germany, most drivers replace Summer tyres with Winter tyres in October and back again in April. Those tyres have different pressures and different rolling diameters compared to the Summer tyres.
Because the system does not have a direct pressure sensor, it needs to be calibrated. That involves driving for 10-15 minutes while the various sensors (in reality the ABS sensors on each wheel) detect the rotation of the wheels and tires and do their comparisons. You are supposed to inflate the tyres correctly before beginning the calibration.
In practice, when the low-pressure warning light comes on, drivers learned to hit the re-calibration button, and that made the warning light switch off – even though the tires might be in a dangerous condition.
Vehicle makers therefore made it more difficult for drivers to simply hit a re-calibration button, and that process now has to be done by a qualified personnel. Or there is a complex set of actions you need to take, so that you cannot reset the system without thinking about the consequences.
Whenever you adjust pressures in any one of the tyres, the iTPMS system needs to be re-calibrated.
Try the Hyundai owners club message boards to see if there is a solution on the boards. This is a very common problem.
The reason the system now tells you that there is a pressure alert is that the balance between the different tyres has changed. And that’s all it knows. It does not know the absolute pressure in each tyre.
I do not know if the garage will charge you for this. It is a safety feature, so in my opinion, they should not, but that opinion is not worth much where garages are concerned.
The alternative is to fit direct TPMS (dTPMS) systems, such as the following, on each tyre
http://www.fit2gotpms.com/michelin/
or these
https://www.nonda.co/products/zus-smart-tire-safety-monitor
These have the advantage that they detect low pressure almost immediately, and can give an absolute read-out.
I have the Nonda system.
Another issue is that tyres lose pressure at a slow rate as air permeates through the sidewalls, so an iTPMS will not detect simultaneous pressure loss in all four tyres. A dTPMS. On the other hand will detect that loss.