Is he sinful and considered an unbeliever who delayed the 'Asr prayer until he heard the Maghrib Adhan from a mosque, then it became clear to him that its timing was incorrect?

A Muslim should be devoted to prayer and approach it diligently and actively when its time arrives. The Prophet, peace and blessings be upon him, condemned those who delay the Asr prayer. Delaying it until after the sun turns yellow (ishraar) places it in the time of necessity according to some scholars, which is not permissible except with a valid excuse. As for delaying it to the extent that a part of it goes outside its prescribed time, that is not permissible. If a person is aware of this and delays the prayer without an excuse, then they are sinful. Missing it entirely is an even greater sin. The view that whoever misses a single prayer is a disbeliever applies to one who intentionally misses it. It appears that the person mentioned did not do so intentionally. A prayer can be caught by catching the opening takbeer within its time.