Since the outbreak of the epidemic, the people of the motherland have always been concerned about the health and safety of overseas compatriots.

Always means the same thing as always. What the author wants to express is that the people of the motherland are always concerned about the health and safety of their overseas compatriots, but they use the wrong words because they don't understand the meaning of the words.

Might as well read:

Since the outbreak of the epidemic, the people of the motherland have always been concerned about the health and safety of overseas compatriots.

or

Since the outbreak, the people of the motherland have always been concerned about the health and safety of overseas compatriots.