You lower the cooling setpoint, and the thermostat moves the heating setpoint too. It may be preserving a required separation between the two targets rather than ignoring your instruction.
The Resideo TH5220D operating manual describes a heat-cool separation called a deadband in its auto-changeover mode. Other products use different algorithms and terms, so read the manual for the installed model before applying that example.
Identify which setting you are changing
A heating target, cooling target, switching differential and equipment protection delay may describe different parts of operation. Similar-looking numbers do not make them interchangeable. Ask an installer to explain any setting whose purpose is unclear.
In a simple conceptual example, heating is requested below one target and cooling above another, leaving a range between them. The actual system may include additional controls and delays. That example explains the idea; it is not a recommended temperature schedule.
Record behaviour before changing more settings
Note the mode, displayed room temperature, requested targets and what the system did. Give it the time specified by its instructions. Repeatedly moving controls can make it harder to understand whether a normal delay or a genuine problem is involved.
If the thermostat will not accept a chosen combination, check whether the manual describes a minimum separation or an installer configuration. Do not enter unfamiliar service menus or alter wiring to force a result.
For persistent discomfort or unexpected heating and cooling, contact a qualified HVAC professional. Explain the observed sequence and any recent changes, including a new thermostat or system service.
Keep the model number and manual accessible. A useful adjustment begins with understanding what the control represents on that device. The word deadband offers a clue, but the installed thermostat’s own documentation determines how the clue applies.