The type of problem your car is having requires systematic diagnostics. Barring any mechanical problems like faulty fans/blowers, leaks, compressor issues and such, the minimum tools of the trade would usually include Toyota's OBDII scanner (TIS Techstream), and a standard room thermometer.

My guess at this point is that it may have something to do with the A/C control module and its sensor(s). Simply put, once a preset temp is entered by the driver, the control unit will do its best to achieve that temp using its own temp sensor. Once the desired temp is achieved, it sends out a signal to disengage the compressor. If the A/C control module is acting up or its sensor has become out-of-spec, or probably even blocked, it can give off the wrong feedback to the controller. Bad info in, bad info out.

Using Toyota's OBDII scanner, the technician may be able to get the temperature that is actually being detected by the A/C temp sensor through the CAN bus (Controller Area Network - The network that makes it possible for different car components like door locks, SRS, A/C, ECM/PCM, etc. to be able talk to each other). The room thermometer can be used to validate the cabin temp. If they're off by several degrees from what the TIS is saying, even after the A/C has been running for several minutes with the car under the shade, I'd swap out that controller and/or sensor for a known good one for testing.

The car's A/C temp sensor is usually behind a grilled opening on the dashboard near the knee area. On the Altis, that would be the small opening besides the Engine Start button. If this is blocked or if the sensor is defective/out-of-spec, or dislodged, it may not read the cabin temp correctly.

I hope you get this sorted out eventually.