My thermostat is set on auto when it calls for heat my ac unit also comes on is this normal

The Auto on most stats just runs the fan when the furn. Or A.C tells it to. The On allows the fan
To run continuously without regard to what the furnace or A.C. are doing. So is the selector only able to select between Auto and ON. Are you certain the outside (condenser) A.C unit is coming on. Is there another switch on the thermostat selectable between Heat/Off/Cool and is it on Cool or Heat.
Or is it a Digital stat selecting between Heat/Cool/Program/Auto/ Off . Auto in this case means auto changeover. Which means it will automatically switch from heat to cool based on the inside room temp. But normally there is a 2 degree differential so both cannot come on. For instance if heating is set to 70, cooling with be at 72 minimum. If you move the stat up to 74 heating then it will automatically bump cooling up to 76. If a stat. was recently replaced was the wiring done correctly,
And both the A.C. and heating circuits are energized.
R is usually low voltage power from the furnace transformer. The stat just selects what you want to turn on. Y is the cooling circuit, G is the fan circuit. If it is a newer Bryant/ Carrier with an Evolution or Infinity control 2 wires are power and 2 act as data.
There could also be a short in the thermostat wires between Y and W if the A.C only comes on during a call for heat.

It can usually be a help if when you post a question you tell us the type,brand,and model numbers of your furnace/equipment and tstat ,that way the people trying to help will have a little more info

By auto, do you mean automatic changeover mode? If you have a heat pump system, the outdoor unit will run in the heating mode. If it isn't a heat pump system, try the t-stat selector in the heat-only position.