AC blowing hot air after being serviced

The dye shows up as a bright yellow stain under a black light. Some AC system dyes do show up as a shiny green stain in natural light, but some cannot be seen without the black light. Also keep in mind refrigerant is lost when it escapes as a vapor. It is possible for the dye to circulate in the system but not make it to a leak.

Two common sources of leaks are the condenser in front of the radiator and the evaporator inside the heater box under the dash. Dye can be almost impossible to see from those places. The dye can be a great tool for very slow leaks, but if your system is going empty in as little as a few weeks, an electronic leak detector is the better tool.

The first thing your mechanic should do is connect a set of gauges to see what the pressures are when the system is running. If they are somewhat normal, the better suspect is the temperature door or actuator in the heater box. Many cars use a computer module to run the mode and temperature doors. Those computers cause more trouble than almost anything else.

Yes. The temperature door blends heated and non-heated or cooled and non-cooled air to get the desired temperature. The mode doors switch where the air blows from.