Vietnamese learners of Japanese stumble over keigo. Japanese learners of Vietnamese stumble over pronouns. These are two sides of one problem.
Japanese changes the verb
Japan's Council for Cultural Affairs reorganised keigo into five categories in its 2007 guidance: respectful, humble I, humble II (courteous), polite, and beautifying forms. It refined the three-way split long taught in schools.
What matters is that respect rides on the shape of the verb. One meaning, "to say", appears as iu, ossharu, mōsu. You need not state the subject; the verb alone shows whom the speaker is elevating.
Vietnamese changes the name
Vietnamese verbs do not conjugate. Respect sits elsewhere: in what you call the person in front of you.
An older man is anh, an older woman chị, someone younger em. Someone of your parents' generation is cô or chú; of your grandparents', ông or bà. And what you call yourself shifts to match: if they are anh, you are em.
Which means that in Vietnamese, you cannot begin a sentence until you have chosen the term.
Hence the question about age
This produces a habit that puzzles Japanese colleagues: Vietnamese speakers often ask your age on first meeting.
It is not prying. Without an age, there is no way to choose between anh and em, and without that choice there is no sentence. The Japanese equivalent would be having to speak before deciding whether to use keigo or plain form.
In Japan, asking someone's age is treated as a step into private territory. Without knowing the reason, the question sounds tactless.
"Dạ" carries no content
One more. The word dạ, which Vietnamese speakers often place at the start of a sentence, has almost no dictionary meaning. It marks politeness.
It is usually translated as "yes", but it does not necessarily signal agreement. It is closer to "I am listening" or "I am being respectful". Hearing dạ does not mean the other person has agreed to what you said.
What this means at work
A Vietnamese employee misusing keigo is not being disrespectful. Their first language simply puts respect somewhere else.
And when asked your age, reading it as information needed to build a sentence rather than as intrusion changes the whole exchange.